Question

solve each inequality and show work.
1) 4x - 2 > 2x + 8

2) -3x - 6 > 4x - 20

3) 4(x + 1) < 3x - 2

4) 2x + 3 + x < -2x + 1 + 12

5) 2(x - 1) > 4x + 4 - 5x

6) 2 + 4x -7 < 8x + 2 - 2x

Answer 1

Answer: Use the app photo math, you just take a picture and it gives you the answer and shows you the steps:)

1) x> 5

2) x< 2

3) x<-6

4) x< 2

5) x> 2

6) x> - 7/2

Step-by-step explanation:

See the images below for the work:)  The images will be in order with the number the first problem will be the answer to the first.

Answer 2

Answer:

$\sf 1)\:4x - 2 > 2x + 8$

Add 2 from both sides:

$\sf 4x-2+2>2x+8+2$

$\sf 4x>2x+10$

Subtract 2x from both sides:

$\sf 4x-2x>2x+10-2x$

$\sf 2x>10$

Divide both sides by 2:

$\sf \cfrac{2x}{2}>\cfrac{10}{2}$

$\boxed{\sf x>5}$

_______________________________

$\sf 2)\: -3x - 6 > 4x - 20$

Add 6 from both sides:

$\sf -3x-6+6>4x-20+6$

$\sf -3x>4x-14$

Subtract 4x from both sides:

$\sf -3x-4x>4x-14-4x$

$\sf -7x>-14$

Multiply both sides by -1:

$\sf\left(-7x\right)\left(-1\right)<\left(-14\right)\left(-1\right)$

$\sf 7x<14$

Divide both sides by 7:

$\sf \cfrac{7x}{7}<\cfrac{14}{7}$

$\boxed{\sf x<2}$

_______________________________

$\sf 3)\: 4(x + 1) < 3x - 2$

Apply distributive property:

$\sf 4x+4<3x-2$

Subtract 4 from both sides:

$\sf 4x+4-4<3x-2-4$

$\sf 4x<3x-6$

Subtract 3x from both sides:

$\sf 4x-3x<3x-6-3x$

$\boxed{\sf x<-6}$

_______________________________

$\sf 4)\: 2x + 3 + x < -2x + 1 + 12$

Combine like terms:

$\sf (2x+x)= 3x$

$\sf( 1+12)=13$

$\sf 3x+3<-2x+13$

Subtract 3 from both sides:

$\sf 3x+3-3<-2x+13-3$

$\sf 3x<-2x+10$

Add 2x from both sides:

$\sf 3x+2x<-2x+10+2x$

$\sf 5x<10$

Divide both sides by 5:

$\sf \cfrac{5x}{5}<\cfrac{10}{5}$

$\boxed{\sf x<2}$

________________________________

$\sf 5)\: 2(x - 1) > 4x + 4 - 5x$

Combine like terms:

$\sf (4x-5x)=-x$

$\sf 2\left(x-1\right)>-x+4$

Apply distributive property:

$\sf 2x-2>-x+4$

Add 2 from both sides:

$\sf 2x-2+2>-x+4+2$

$\sf 2x>-x+6$

Add x from both sides:

$\sf 2x+x>-x+6+x$

$\sf 3x>6$

Divide both sides by 3:

$\sf \cfrac{3x}{3}>\cfrac{6}{3}$

$\boxed{\sf x>2}$

_______________________________

$\sf 6)\: 2 + 4x -7 < 8x + 2 - 2x$

Subtract 2 from both sides:

$\sf 2+4x-7-2<8x+2-2x-2$

$\sf 4x-7<8x-2x$

Combine like terms:

$\sf (8x-2x)=6x$

$\sf 4x-7<6x$

Add 7 from both sides:

$\sf 4x-7+7<6x+7$

$\sf 4x<6x+7$

Subtract 6x from both sides:

$\sf 4x-6x<6x+7-6x$

$\sf -2x<7$

Multiply both sides by -1:

$\sf \left(-2x\right)\left(-1\right)>7\left(-1\right)$

$\sf 2x>-7$

Divide both sides by 2:

$\sf \cfrac{2x}{2}>\cfrac{-7}{2}$

$\boxed{\sf x>-\frac{7}{2}}$

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