Question

Solve the inequality for x. Show each step of the solution.

12(x+3)>4x-8

Answer 1

`{ \boxed{ \pink{ \sf{x > - (11)/(2)}}}}`

Explanation:

The given inequality is,
`{ \green{ \sf{12(x + 3) > 4x - 8}}}`

`{ \star}`Step 1: Simplify both the sides of inequality.

`{ \green{ \sf{12x + 36 > 4x - 8}}}`

`{ \star}`Step 2: Now Subtract 4x from both sides.

`{ \purple{ \sf{12x+36−4x> { \cancel{4x}−8{ \cancel{−4x}}}}}}`

`{ \purple{ \sf{8x+36>−8}}}`

`{ \star}`Step 3: Subtract 36 from both sides.

`{ \blue{ \sf{8x+{ \cancel{36}{ \cancel{−36}}}>−8−36}}}`

`{ \blue{ \sf{8x>−44}}}`

`{ \star}`Step 4: Divide both sides by 8.

`{ \orange{ \sf{ ( \cancel8)/( \cancel8) x > - \frac{ \cancel{44^{ \blue{ \tt{11}}}} }{ \cancel8_{ \blue{ \tt{2}}} }}}}`

`{ \boxed{ \red{ \sf{x > - (11)/(2)}}}}`

Answer 2

Explanation:

Step 1: Simplify both sides of the inequality.

12x+36>4x−8

Step 2: Subtract 4x from both sides.

12x+36−4x>4x−8−4x

8x+36>−8

Step 3: Subtract 36 from both sides.

8x+36−36>−8−36

8x>−44

Step 4: Divide both sides by 8.

8x/8 > -44/8

Therefore your answer will now equal
`x > (-11)/(2)`