Solve 7.2(3x-1)-3(4x+5)leqx-4(x-7)

$$7.2 ( 3 x - 1 ) - 3 ( 4 x + 5 ) \leq x - 4 ( x - 7 )$$

Solve for x

$$x\leq \frac{251}{63}$$

Solution Steps

Use the distributive property to multiply 7.2 by 3x-1.

$$21.6x-7.2-3\left(4x+5\right)\leq x-4\left(x-7\right)$$

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

$$21.6x-7.2-12x-15\leq x-4\left(x-7\right)$$

Combine 21.6x and -12x to get 9.6x.

$$9.6x-7.2-15\leq x-4\left(x-7\right)$$

Subtract 15 from -7.2 to get -22.2.

$$9.6x-22.2\leq x-4\left(x-7\right)$$

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

$$9.6x-22.2\leq x-4x+28$$

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

$$9.6x-22.2\leq -3x+28$$

Add 3x to both sides.

$$9.6x-22.2+3x\leq 28$$

Combine 9.6x and 3x to get 12.6x.

$$12.6x-22.2\leq 28$$

Add 22.2 to both sides.

$$12.6x\leq 28+22.2$$

Add 28 and 22.2 to get 50.2.

$$12.6x\leq 50.2$$

Divide both sides by 12.6. Since 12.6 is positive, the inequality direction remains the same.

$$x\leq \frac{50.2}{12.6}$$

Expand \frac{50.2}{12.6} by multiplying both numerator and the denominator by 10.

$$x\leq \frac{502}{126}$$

Reduce the fraction \frac{502}{126} to lowest terms by extracting and canceling out 2.

$$x\leq \frac{251}{63}$$