Solve -4(x-3)+8xgeq7*(x-7)

$$- 4 ( x - 3 ) + 8 x \geq 7 \cdot ( x - 7 )$$

Solve for x

$$x\leq \frac{61}{3}$$

Solution Steps

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

$$-4x+12+8x\geq 7\left(x-7\right)$$

Combine -4x and 8x to get 4x.

$$4x+12\geq 7\left(x-7\right)$$

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

$$4x+12\geq 7x-49$$

Subtract 7x from both sides.

$$4x+12-7x\geq -49$$

Combine 4x and -7x to get -3x.

$$-3x+12\geq -49$$

Subtract 12 from both sides.

$$-3x\geq -49-12$$

Subtract 12 from -49 to get -61.

$$-3x\geq -61$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-61}{-3}$$

Fraction \frac{-61}{-3} can be simplified to \frac{61}{3} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{61}{3}$$