Question

3(2x – 1) < 2(4 + 3x)

Answer 1

for every value of x

Explanation:

6x - 3 < 8 + 6x

6x - 6x < 3 + 8

0 < 5

always

Answer 2

Answer: Infinite Solutions

Explanation:

In order to solve the inequality, isolate x.

Given inequality:

`\star\quad\sf{3(2x-1) < 2(4+3x)}`

Use the distributive property:

`\star\quad\sf{6x-3 < 8+6x}`

Add 3 to both sides

`\star\quad\sf{6x < 8+3+6x}`

`\star\quad\sf{6x < 11+6x}`

Subtract 6x from both sides

`\star\quad\sf{6x-6x < 11}`

`\star\quad\sf{0x < 11}`

`\star\quad\sf{0 < 11}`

Since 0 is less than 11, this statement is true - and we know that any value of x will satisfy the inequality. Therefore, it has infinite solutions.