Question

1. what is the solution to the equation

$\frac{1}{8}x+\frac{3}{4}x = 21$?
$circled{a}x = 22$
$circled{b}x = 24$
$circled{c}x = 34$
$circled{d}x = 63$
assessment, fo

Explanation:

Step1: Combine like terms

First, find a common denominator for \(\frac{1}{8}x\) and \(\frac{3}{4}x\). The common denominator of \(8\) and \(4\) is \(8\). Rewrite \(\frac{3}{4}x\) as \(\frac{6}{8}x\). Then \(\frac{1}{8}x+\frac{3}{4}x=\frac{1 + 6}{8}x=\frac{7}{8}x\). So the equation becomes \(\frac{7}{8}x = 21\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\frac{7}{8}x=21\) by \(\frac{8}{7}\) (the reciprocal of \(\frac{7}{8}\)). Using the property \(x=a\times\frac{b}{a}\) (where \(a=\frac{7}{8}\) and \(b = 21\)), we have \(x=21\times\frac{8}{7}\). Since \(21\div7 = 3\), then \(x=3\times8\).

Answer:

B. \(x = 24\)