a ) \( -510+302=x \) b) \( -150+x=0 \) c ) \( 14-65=-25+x \) d) \( -86-x=-110 \) e ) \( x-2 x=35 \) f) \( 5 x=-85 \) Which of the following are like term a ) \( 3 b c ; 2 a b ;-12 a c ; 8 a b \) b) \( x^{2} y ;-3 x y ; 13 x ; 12 y ; 9 x y ; 4 x y^{2} \) c) \( 11 a b ; 10 a^{2} b ;-6 a b^{2} ;-a^{2} b \) d) \( 2\left(3 x y^{2}\right) ;-4\left(5 x^{2} y\right) ;-6(4 x y) ;-x(x y \) e) \( a(a b) ; b(a b) ; 2 a(b a) ;-3 b(2 a) \)

Solve the equation by following steps: - step0: Solve for \(x\): \(-510+302=x\) - step1: Add the numbers: \(-208=x\) - step2: Swap the sides: \(x=-208\) Solve the equation \( -150+x=0 \). Solve the equation by following steps: - step0: Solve for \(x\): \(-150+x=0\) - step1: Move the constant to the right side: \(x=0+150\) - step2: Remove 0: \(x=150\) Solve the equation \( 14-65=-25+x \). Solve the equation by following steps: - step0: Solve for \(x\): \(14-65=-25+x\) - step1: Subtract the numbers: \(-51=-25+x\) - step2: Swap the sides: \(-25+x=-51\) - step3: Move the constant to the right side: \(x=-51+25\) - step4: Add the numbers: \(x=-26\) Solve the equation \( -86-x=-110 \). Solve the equation by following steps: - step0: Solve for \(x\): \(-86-x=-110\) - step1: Move the constant to the right side: \(-x=-110+86\) - step2: Add the numbers: \(-x=-24\) - step3: Change the signs: \(x=24\) Solve the equation \( x-2 x=35 \). Solve the equation by following steps: - step0: Solve for \(x\): \(x-2x=35\) - step1: Subtract the terms: \(-x=35\) - step2: Change the signs: \(x=-35\) Solve the equation \( 5 x=-85 \). Solve the equation by following steps: - step0: Solve for \(x\): \(5x=-85\) - step1: Divide both sides: \(\frac{5x}{5}=\frac{-85}{5}\) - step2: Divide the numbers: \(x=-17\) Let's solve the equations step by step and identify like terms. ### Solving the Equations 1. **Equation a:** \[ -510 + 302 = x \] \[ x = -510 + 302 = -208 \] 2. **Equation b:** \[ -150 + x = 0 \] \[ x = 150 \] 3. **Equation c:** \[ 14 - 65 = -25 + x \] \[ -51 = -25 + x \implies x = -51 + 25 = -26 \] 4. **Equation d:** \[ -86 - x = -110 \] \[ -x = -110 + 86 \implies x = 24 \] 5. **Equation e:** \[ x - 2x = 35 \] \[ -x = 35 \implies x = -35 \] 6. **Equation f:** \[ 5x = -85 \] \[ x = -\frac{85}{5} = -17 \] ### Summary of Solutions - a) \( x = -208 \) - b) \( x = 150 \) - c) \( x = -26 \) - d) \( x = 24 \) - e) \( x = -35 \) - f) \( x = -17 \) ### Identifying Like Terms Now, let's identify the like terms in each set: 1. **Set a:** \( 3bc, 2ab, -12ac, 8ab \) - Like terms: \( 2ab, 8ab \) (both have \( ab \)) 2. **Set b:** \( x^2y, -3xy, 13x, 12y, 9xy, 4xy^2 \) - Like terms: \( -3xy, 9xy, 4xy^2 \) (all have \( xy \) but \( 4xy^2 \) is not a direct like term) 3. **Set c:** \( 11ab, 10a^2b, -6ab^2, -a^2b \) - Like terms: \( 11ab, -6ab^2 \) (both have \( ab \)) 4. **Set d:** \( 2(3xy^2), -4(5x^2y), -6(4xy), -x(xy) \) - Like terms: \( 2(3xy^2), -6(4xy) \) (both have \( xy \)) 5. **Set e:** \( a(ab), b(ab), 2a(ba), -3b(2a) \) - Like terms: \( a(ab), b(ab), 2a(ba) \) (all have \( ab \)) ### Summary of Like Terms - a) \( 2ab, 8ab \) - b) \( -3xy, 9xy \) (not direct like terms with \( 4xy^2 \)) - c) \( 11ab, -6ab^2 \) - d) \( 2(3xy^2), -6(4xy) \) - e) \( a(ab), b(ab), 2a(ba) \) If you need further assistance or clarification, feel free to ask!