Question

1. factor $-\frac{1}{2}$ out of $-\frac{1}{2}x + 8$.
2. the area of the rectangle is $(18x - 12)$ square inches. write an expression

that represents the length of the rectangle (in inches).
6 in.

Explanation:

Step1: Factor out \(-\frac{1}{2}\) from \(-\frac{1}{2}x\)

When we factor out \(-\frac{1}{2}\) from \(-\frac{1}{2}x\), we get \(x\) since \(\frac{-\frac{1}{2}x}{-\frac{1}{2}}=x\)

Step2: Factor out \(-\frac{1}{2}\) from \(8\)

We know that \(8\div(-\frac{1}{2})=8\times(- 2)=-16\)

Step3: Write the factored form

The original expression \(-\frac{1}{2}x + 8\) can be written as \(-\frac{1}{2}(x - 16)\)

Step1: Recall the formula for the area of a rectangle

The area of a rectangle \(A = l\times w\), where \(A\) is the area, \(l\) is the length and \(w\) is the width. Given \(A=(18x - 12)\) and \(w = 6\)

Step2: Solve for \(l\)

We use the formula \(l=\frac{A}{w}\). Substitute \(A=(18x - 12)\) and \(w = 6\) into the formula: \(\frac{18x-12}{6}\)

Step3: Simplify the expression

We can split the fraction \(\frac{18x-12}{6}=\frac{18x}{6}-\frac{12}{6}\)
Since \(\frac{18x}{6}=3x\) and \(\frac{12}{6} = 2\)

Answer:

\(-\frac{1}{2}(x - 16)\)

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For problem 19: