Question
23. Given \( g(x)=-\frac{3}{2} x-9 \), if \( g(x)=-48 \), find \( x \).
Ask by Riley Adkins. in Guam
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 26 \)
Solution
Solve the equation \( -\frac{3}{2}x-9=-48 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(-\frac{3}{2}x-9=-48\)
- step1: Move the constant to the right side:
\(-\frac{3}{2}x=-48+9\)
- step2: Add the numbers:
\(-\frac{3}{2}x=-39\)
- step3: Change the signs:
\(\frac{3}{2}x=39\)
- step4: Multiply by the reciprocal:
\(\frac{3}{2}x\times \frac{2}{3}=39\times \frac{2}{3}\)
- step5: Multiply:
\(x=26\)
The value of \( x \) when \( g(x) = -48 \) is \( x = 26 \).
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Simplify this solution Mind Expander
To solve for \( x \) in the equation \( g(x) = -48 \), we start with the given function \( g(x) = -\frac{3}{2} x - 9 \). Setting the function equal to \(-48\): \[ -\frac{3}{2} x - 9 = -48 \] Next, we can isolate \( x \) by first adding 9 to both sides: \[ -\frac{3}{2} x = -48 + 9 \] \[ -\frac{3}{2} x = -39 \] Now, we multiply both sides by \(-\frac{2}{3}\) to solve for \( x \): \[ x = -39 \times -\frac{2}{3} \] \[ x = 26 \] Thus, the solution is \( x = 26 \).
