Pre-Algebra Examples

$\frac{3 x - 2}{4} > 2 - x$

Step 1

Multiply both sides by $4$ .

$\frac{3 x - 2}{4} \cdot 4 > (2 - x) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{3 x - 2}{4} \cdot 4 > (2 - x) \cdot 4$

Step 2.1.1.2

Rewrite the expression.

$3 x - 2 > (2 - x) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(2 - x) \cdot 4$ .

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Step 2.2.1.1

Apply the distributive property.

$3 x - 2 > 2 \cdot 4 - x \cdot 4$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Multiply $2$ by $4$ .

$3 x - 2 > 8 - x \cdot 4$

Step 2.2.1.2.2

Multiply $4$ by $- 1$ .

$3 x - 2 > 8 - 4 x$

Step 2.2.1.2.3

Reorder $8$ and $- 4 x$ .

$3 x - 2 > - 4 x + 8$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the inequality.

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Step 3.1.1

Add $4 x$ to both sides of the inequality.

$3 x - 2 + 4 x > 8$

Step 3.1.2

Add $3 x$ and $4 x$ .

$7 x - 2 > 8$

Step 3.2

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

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Step 3.2.1

Add $2$ to both sides of the inequality.

$7 x > 8 + 2$

Step 3.2.2

Add $8$ and $2$ .

$7 x > 10$

Step 3.3

Divide each term in $7 x > 10$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 x > 10$ by $7$ .

$\frac{7 x}{7} > \frac{10}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} > \frac{10}{7}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x > \frac{10}{7}$

Step 4