Chapter 6, Problem 1R

Solve each equation and check:

$2x+4=7$

To determine

To calculate: The solution of the equation $2x+4=7$ and check it.

Answer to Problem 1R

Solution:

The solution of the equation $2x+4=7$ is $\underset{\_}{\frac{3}{2}}$.

Explanation of Solution

Given Information:

The provided equation is $2x+4=7$.

Formula used:

Subtraction property:

The resultant equation will be equivalent to the original equation, if the same quantity is subtracted on both sides of the equation.

Division property:

The resultant equation will be equivalent to the original equation, if the same non-zero quantity is divided on both sides of the equation.

Calculation:

Consider the provided equation.

$2x+4=7$

Apply the subtraction property stated above, subtract both sides of the equation by 4.

$\begin{array}{l}2x+4-4=7-4\\ 2x=3\end{array}$

Apply the division property stated above, divide both sides of the equation by 2.

$\begin{array}{l}\frac{2x}{2}=\frac{3}{2}\\ x=\frac{3}{2}\end{array}$

Check:

Substitute $\frac{3}{2}$ for $x$ in the original equation.

$\begin{array}{l}2\left(\frac{3}{2}\right)+4\stackrel{?}{=}7\\ 3+4\stackrel{?}{=}7\\ 7=7\end{array}$

Which is true.

Hence, the solution of the equation $2x+4=7$ is $\frac{3}{2}$.