QuestionExample 1 Solve each equation. Check
1. $7 x+8(x-3)=12-3 x$

Studdy Solution

STEP 1

1. The equation $7x + 8(x - 3) = 12 - 3x$ is a linear equation in one variable.
2. The goal is to find the value of $x$ that satisfies the equation.
3. We will use basic algebraic operations such as distribution, combining like terms, and isolating the variable.

STEP 2

1. Simplify both sides of the equation.
2. Combine like terms.
3. Isolate the variable $x$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $8$ on the left-hand side of the equation:
$7x + 8(x - 3) = 12 - 3x$
$7x + 8x - 24 = 12 - 3x$

STEP 4

Combine like terms on the left-hand side:
$(7x + 8x) - 24 = 12 - 3x$
$15x - 24 = 12 - 3x$

STEP 5

Add $3x$ to both sides to start isolating $x$ :
$15x - 24 + 3x = 12 - 3x + 3x$
$18x - 24 = 12$

STEP 6

Add $24$ to both sides to further isolate $x$ :
$18x - 24 + 24 = 12 + 24$
$18x = 36$

STEP 7

Divide both sides by $18$ to solve for $x$ :
$\frac{18x}{18} = \frac{36}{18}$
$x = 2$

STEP 8

Check the solution by substituting $x = 2$ back into the original equation:
Original equation: $7x + 8(x - 3) = 12 - 3x$
Substitute $x = 2$ :
$7(2) + 8(2 - 3) = 12 - 3(2)$

STEP 9

Simplify both sides:
Left side: $14 + 8(-1) = 14 - 8 = 6$
Right side: $12 - 6 = 6$
Both sides are equal, confirming that $x = 2$ is the correct solution.
The solution is:
$\boxed{2}$

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