Algebra Examples

$\frac{(4 x - 3)}{7} < 6$

Step 1

Solve $x < \frac{45}{4}$ .

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Step 1.1

Multiply both sides by $7$ .

$\frac{4 x - 3}{7} \cdot 7 < 6 \cdot 7$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Cancel the common factor of $7$ .

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Step 1.2.1.1.1

Cancel the common factor.

$\frac{4 x - 3}{7} \cdot 7 < 6 \cdot 7$

Step 1.2.1.1.2

Rewrite the expression.

$4 x - 3 < 6 \cdot 7$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Multiply $6$ by $7$ .

$4 x - 3 < 42$

Step 1.3

Solve for $x$ .

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Step 1.3.1

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

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Step 1.3.1.1

Add $3$ to both sides of the inequality.

$4 x < 42 + 3$

Step 1.3.1.2

Add $42$ and $3$ .

$4 x < 45$

Step 1.3.2

Divide each term in $4 x < 45$ by $4$ and simplify.

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Step 1.3.2.1

Divide each term in $4 x < 45$ by $4$ .

$\frac{4 x}{4} < \frac{45}{4}$

Step 1.3.2.2

Simplify the left side.

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Step 1.3.2.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} < \frac{45}{4}$

Step 1.3.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{45}{4}$

Step 2

Use the inequality $x < \frac{45}{4}$ to build the set notation.

${x | x < \frac{45}{4}}$

Step 3