How do you solve the inequality: #-5(13x + 3)

Question

How do you solve the inequality: #-5(13x + 3) < - 2(13x - 3)#?

Nathan Axel · Accepted Answer

#x in (-7/13, + oo)#

Start by dividing both sides of the inequality by #(-1)# - do not forget to change the sign of the inequality when you do this

#(-5(13x + 3))/((-1)) > (-2(13x - 3))/((-1))#

#5(13x + 3) > 2(13x - 3)#

Next, use the distributive property of multiplication to expand the two parantheses

# 5 * 13x + 5 * 3 > 2 * 13x + 2 * (-3)#

#65x + 15 > 26x - 6#

Rearrange to get the #x#-term on one side of the inequality

#65x - 26x > -6 - 15#

#39x > - 21 implies x > -21/39 = -7/13#

This means that your inequality will be true for any value of #x# that is greater than #-7/13#. The solution set for this inequality will be #x in (-7/13, + oo)#.

Isaiah Anthony · Answer

undefined To solve the inequality -5(13x + 3) < -2(13x - 3), first distribute the -5 and -2: -5 * 13x = -65x -5 * 3 = -15 -2 * 13x = -26x -2 * -3 = 6 Then, rewrite the inequality: -65x - 15 < -26x + 6 Subtract -26x from both sides: -65x - 26x - 15 < 6 Combine like terms: -91x - 15 < 6 Add 15 to both sides: -91x < 21 Divide both sides by -91 (remember to flip the inequality sign when dividing by a negative number): x > -21/91 So, the solution to the inequality is x > -21/91.

How do you solve the inequality: #-5(13x + 3) &lt; - 2(13x - 3)#?

How do you solve the inequality: #-5(13x + 3) < - 2(13x - 3)#?