Solve 8(x-2)/7<3/4

$$\frac { 8 ( x - 2 ) } { 7 } < \frac { 3 } { 4 }$$

Solve for x

$$x<\frac{85}{32}$$

Solution Steps

Multiply both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$8\left(x-2\right)<\frac{3}{4}\times 7$$

Use the distributive property to multiply 8 by x-2.

$$8x-16<\frac{3}{4}\times 7$$

Express \frac{3}{4}\times 7 as a single fraction.

$$8x-16<\frac{3\times 7}{4}$$

Multiply 3 and 7 to get 21.

$$8x-16<\frac{21}{4}$$

Add 16 to both sides.

$$8x<\frac{21}{4}+16$$

Convert 16 to fraction \frac{64}{4}.

$$8x<\frac{21}{4}+\frac{64}{4}$$

Since \frac{21}{4} and \frac{64}{4} have the same denominator, add them by adding their numerators.

$$8x<\frac{21+64}{4}$$

Add 21 and 64 to get 85.

$$8x<\frac{85}{4}$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x<\frac{\frac{85}{4}}{8}$$

Express \frac{\frac{85}{4}}{8} as a single fraction.

$$x<\frac{85}{4\times 8}$$

Multiply 4 and 8 to get 32.

$$x<\frac{85}{32}$$