Sure! Let's solve the equation [tex]\( 5x + 2 = x + 7 \)[/tex] step-by-step.
1. Eliminate the variable [tex]\( x \)[/tex] from one side of the equation:
We start by subtracting [tex]\( x \)[/tex] from both sides of the equation to simplify it.
[tex]\[
5x + 2 - x = x + 7 - x
\][/tex]
Simplifying this, we get:
[tex]\[
4x + 2 = 7
\][/tex]
2. Isolate the term with the variable [tex]\( x \)[/tex]:
Next, we need to get rid of the constant term on the left side. We do this by subtracting 2 from both sides of the equation.
[tex]\[
4x + 2 - 2 = 7 - 2
\][/tex]
Simplifying this, we get:
[tex]\[
4x = 5
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Finally, we solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 4.
[tex]\[
x = \frac{5}{4}
\][/tex]
Therefore, the solution to the equation [tex]\( 5x + 2 = x + 7 \)[/tex] is:
[tex]\[
x = \frac{5}{4}
\][/tex]
So, [tex]\( x = 1.25 \)[/tex] in decimal form. This means the value of [tex]\( x \)[/tex] that satisfies the original equation is [tex]\( \frac{5}{4} \)[/tex].
