Question
\begin{tabular}{l} Solve \\ \( \qquad \begin{array}{l}6 x-(2 x-3)=31 \\ x^{2}+2 x-15=0\end{array} \) \\ \hline\end{tabular}
Ask by Kelly Tyler. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \( x = 7 \), \( x = -5 \), and \( x = 3 \).
Solution
Solve the equation \( 6x-(2x-3)=31 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(6x-\left(2x-3\right)=31\)
- step1: Subtract the terms:
\(4x+3=31\)
- step2: Move the constant to the right side:
\(4x=31-3\)
- step3: Subtract the numbers:
\(4x=28\)
- step4: Divide both sides:
\(\frac{4x}{4}=\frac{28}{4}\)
- step5: Divide the numbers:
\(x=7\)
Solve the equation \( x^{2}+2x-15=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}+2x-15=0\)
- step1: Factor the expression:
\(\left(x-3\right)\left(x+5\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-3=0\\&x+5=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=3\\&x=-5\end{align}\)
- step4: Rewrite:
\(x_{1}=-5,x_{2}=3\)
The solutions to the system of equations are \( x = 7 \) and \( x = -5 \) or \( x = 3 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the first equation \( 6x - (2x - 3) = 31 \), let's simplify it step-by-step. First, distribute the negative sign: \[ 6x - 2x + 3 = 31 \] Next, combine like terms: \[ 4x + 3 = 31 \] Now, subtract 3 from both sides: \[ 4x = 28 \] Finally, divide by 4: \[ x = 7 \] Now onto the second equation \( x^2 + 2x - 15 = 0 \). We can factor this quadratic equation: \[ (x + 5)(x - 3) = 0 \] Setting each factor to zero gives us: \[ x + 5 = 0 \quad \Rightarrow \quad x = -5 \] \[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \] So, the solutions to the equations are \( x = 7 \) for the first equation, and \( x = -5 \) or \( x = 3 \) for the second equation.
