Login
Premium
Home Question Bank Math Algebra
Question
upstudy study bank question image url

Determine which of the following points are included in the solution set to the following linear inequality. \[ \begin{array}{l}-4 x+5 y \geq-3\end{array} \] Answer \( \square(0,0) \) \( \square(7,2) \) \( \square(-2,-3) \) \( \square(-2,2) \) \( \square\left(3, \frac{9}{5}\right) \)

Ask by Pollard Paul. in the United States
Jan 20,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The points \((0, 0)\), \((-2, 2)\), and \(\left(3, \frac{9}{5}\right)\) satisfy the inequality \(-4x + 5y \geq -3\).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Reviewed and approved by the UpStudy tutoring team

Bonus Knowledge

Let’s check each point to see if it satisfies the inequality \(-4x + 5y \geq -3\). For the point \((0,0)\): \(-4(0) + 5(0) \geq -3\) \(0 \geq -3\) (True) ✅ For the point \((7,2)\): \(-4(7) + 5(2) \geq -3\) \(-28 + 10 \geq -3\) \(-18 \geq -3\) (False) ❌ For the point \((-2,-3)\): \(-4(-2) + 5(-3) \geq -3\) \(8 - 15 \geq -3\) \(-7 \geq -3\) (False) ❌ For the point \((-2,2)\): \(-4(-2) + 5(2) \geq -3\) \(8 + 10 \geq -3\) \(18 \geq -3\) (True) ✅ For the point \(\left(3, \frac{9}{5}\right)\): \(-4(3) + 5\left(\frac{9}{5}\right) \geq -3\) \(-12 + 9 \geq -3\) \(-3 \geq -3\) (True) ✅ So, the points included in the solution set are: - \((0,0)\) - \((-2,2)\) - \(\left(3, \frac{9}{5}\right)\)

Related Questions

1. Find the products. a) \( (x+2)(x+3) \) c) \( (a-2)(a+3) \) e) \( (2 y+5)(3 y-2) \) g) \( (2 a-3)(3 a-2) \) i) \( (x-3)(x-2) \) k) \( (2 x-3 y)(2 x+4 y) \) m) \( (7 x+3 y)(2 x-4 y) \)
Algebra South Africa Jan 22, 2025
4. \( \frac{2 x-1}{3}-\frac{4 x-8}{6} \) 6. \( \frac{3}{x-1}+\frac{1}{1-x} \) 8. \( \frac{x}{x+y}+\frac{y}{x-y} \) 10. \( \frac{x+3}{x-3}-\frac{x-3}{x+3} \) 12. \( \frac{5}{3(a-b)}+\frac{3}{2(b-a)} \) 14. \( \frac{x}{x^{2}-y^{2}}+\frac{y}{y^{2}-x^{2}} \) 16. \( \frac{4 x}{(x+y)^{2}}-\frac{4}{x+y} \) 18. \( \frac{3 a}{9 a^{2}-4 b^{2}}-\frac{1}{3 a+2 b} \) 20. \( \frac{2 y}{(x-2 y)^{2}}+\frac{1}{x-2 y} \)
Algebra United States Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { (b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { 1) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b)\end{array} \)
Algebra South Africa Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { \b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { \l) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b) \\ \text { 2. Find the products. } & \text { b) }(a+3)(a+4) \\ \text { a) }(x+1)(x+3) & \text { (d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { (e) }(3 x y+2 z)(2 x y-3 z) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { k) }(2 a-b)(2 a+b) & \text { n) }(x+3)^{2} \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \end{array} \)
Algebra South Africa Jan 22, 2025
2. Find the products. \( \begin{array}{ll}\text { a) }(x+1)(x+3) & \text { b) }(a+3)(a+4) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { e) }(3 x y+2 z)(2 x y-3 z) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { k) }(2 a-b)(2 a+b) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \text {-n) }(x+3)^{2}\end{array} \)
Algebra South Africa Jan 22, 2025

Latest Algebra Questions

2. Find the products. \( \begin{array}{ll}\text { a) }(x+1)(x+3) & \text { b) }(a+3)(a+4) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { e) }(3 x y+2 z)(2 x y-3 z) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { k) }(2 a-b)(2 a+b) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \text {-n) }(x+3)^{2}\end{array} \)
Algebra South Africa Jan 22, 2025
5. \( \begin{aligned} j-9 \pi= & 12 \pi \\ +9 \pi & +9 \pi\end{aligned} \)
Algebra United States Jan 22, 2025
7 Expand and simplify \( 5 x(3 x+4)(2 x-1) \)
Algebra United Arab Emirates Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { (b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { 1) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b)\end{array} \)
Algebra South Africa Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { \b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { \l) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b) \\ \text { 2. Find the products. } & \text { b) }(a+3)(a+4) \\ \text { a) }(x+1)(x+3) & \text { (d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { (e) }(3 x y+2 z)(2 x y-3 z) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { k) }(2 a-b)(2 a+b) & \text { n) }(x+3)^{2} \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \end{array} \)
Algebra South Africa Jan 22, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy