Question $5(3 x+4)+2=37$

Studdy Solution

STEP 1

1. The equation $5(3x + 4) + 2 = 37$ is a linear equation in one variable.
2. The goal is to solve for the variable $x$ .
3. The equation involves basic algebraic operations, including distribution, addition, and division.

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Isolate the variable $x$ by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

First, distribute the $5$ across the terms inside the parentheses:
$5 \times 3x + 5 \times 4 = 15x + 20$
Now the equation becomes:
$15x + 20 + 2 = 37$
Combine the constant terms on the left side:
$15x + 22 = 37$

STEP 4

Subtract $22$ from both sides of the equation to begin isolating $x$ :
$15x + 22 - 22 = 37 - 22$
This simplifies to:
$15x = 15$

STEP 5

Divide both sides by $15$ to solve for $x$ :
$\frac{15x}{15} = \frac{15}{15}$
This simplifies to:
$x = 1$

STEP 6

Check the solution by substituting $x = 1$ back into the original equation:
$5(3(1) + 4) + 2 = 37$
Simplify inside the parentheses:
$5(3 + 4) + 2 = 37$
$5(7) + 2 = 37$
$35 + 2 = 37$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{1}$

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