Question

1. solve. write as a decimal.\\(\frac{2x + 5}{4}=7\\)\\(x = \square\\)

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation \(\frac{2x + 5}{4}=7\) by \(4\) to get rid of the denominator on the left - hand side. According to the multiplication property of equality, if \(a = b\), then \(a\times c=b\times c\) (where \(c = 4\) in this case). So we have \((\frac{2x + 5}{4})\times4=7\times4\), which simplifies to \(2x+5 = 28\).

Step2: Isolate the term with \(x\)

Subtract \(5\) from both sides of the equation \(2x + 5=28\) to isolate the term with \(x\). According to the subtraction property of equality, if \(a + b=c\), then \(a + b-b=c - b\). So \(2x+5 - 5=28 - 5\), which simplifies to \(2x=23\).

Step3: Solve for \(x\)

Divide both sides of the equation \(2x = 23\) by \(2\) to solve for \(x\). According to the division property of equality, if \(a\times b=c\), then \(\frac{a\times b}{b}=\frac{c}{b}\) (where \(b = 2\) in this case). So \(x=\frac{23}{2}\).

Step4: Convert to decimal

To convert \(\frac{23}{2}\) to a decimal, we know that \(\frac{23}{2}=23\div2\). Performing the division \(23\div2 = 11.5\).

Answer:

\(11.5\)