Pre-Algebra Examples

$3 x + 4 = 7$ , $3 x - 8 = 1$

Step 1

Solve for $x$ in $3 x + 4 = 7$ .

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Step 1.1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1.1

Subtract $4$ from both sides of the equation.

$3 x = 7 - 4$

$3 x - 8 = 1$

Step 1.1.2

Subtract $4$ from $7$ .

$3 x = 3$

$3 x - 8 = 1$

$3 x = 3$

$3 x - 8 = 1$

Step 1.2

Divide each term in $3 x = 3$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x = 3$ by $3$ .

$\frac{3 x}{3} = \frac{3}{3}$

$3 x - 8 = 1$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{3}{3}$

$3 x - 8 = 1$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{3}$

$3 x - 8 = 1$

$x = \frac{3}{3}$

$3 x - 8 = 1$

$x = \frac{3}{3}$

$3 x - 8 = 1$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $3$ by $3$ .

$x = 1$

$3 x - 8 = 1$

$x = 1$

$3 x - 8 = 1$

$x = 1$

$3 x - 8 = 1$

$x = 1$

$3 x - 8 = 1$

Step 2

Replace all occurrences of $x$ with $1$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 x - 8 = 1$ with $1$ .

$3 (1) - 8 = 1$

$x = 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (1) - 8$ .

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Step 2.2.1.1

Multiply $3$ by $1$ .

$3 - 8 = 1$

$x = 1$

Step 2.2.1.2

Subtract $8$ from $3$ .

$- 5 = 1$

$x = 1$

$- 5 = 1$

$x = 1$

$- 5 = 1$

$x = 1$

$- 5 = 1$

$x = 1$

Step 3

Since $- 5 = 1$ is not true, there is no solution.

No solution

Step 4