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

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

`\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>-(7)/(2)}`

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