Solve 72(3x-1)-3(4x+5)leqx-4(x-7)

$$72 ( 3 x - 1 ) - 3 ( 4 x + 5 ) \leq x - 4 ( x - 7 )$$

Solve for x

$$x\leq \frac{5}{9}$$

Solution Steps

Use the distributive property to multiply 72 by 3x-1.

$$216x-72-3\left(4x+5\right)\leq x-4\left(x-7\right)$$

Use the distributive property to multiply -3 by 4x+5.

$$216x-72-12x-15\leq x-4\left(x-7\right)$$

Combine 216x and -12x to get 204x.

$$204x-72-15\leq x-4\left(x-7\right)$$

Subtract 15 from -72 to get -87.

$$204x-87\leq x-4\left(x-7\right)$$

Use the distributive property to multiply -4 by x-7.

$$204x-87\leq x-4x+28$$

Combine x and -4x to get -3x.

$$204x-87\leq -3x+28$$

Add 3x to both sides.

$$204x-87+3x\leq 28$$

Combine 204x and 3x to get 207x.

$$207x-87\leq 28$$

Add 87 to both sides.

$$207x\leq 28+87$$

Add 28 and 87 to get 115.

$$207x\leq 115$$

Divide both sides by 207. Since 207 is positive, the inequality direction remains the same.

$$x\leq \frac{115}{207}$$

Reduce the fraction \frac{115}{207} to lowest terms by extracting and canceling out 23.

$$x\leq \frac{5}{9}$$