Question

3x-7<_4 (x+2); x/2+3-x/4 <2 ​

Answer 1

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Answer 2

Let's solve these two inequalities step by step:

1. 3x - 7 ≤ 4(x + 2)

First, distribute 4 on the right side of the inequality:

3x - 7 ≤ 4x + 8

Now, move 3x to the right side by subtracting 3x from both sides:

-7 ≤ x + 8

Next, move 8 to the left side by subtracting 8 from both sides:

-7 - 8 ≤ x

-15 ≤ x

So, the solution to the first inequality is x ≤ -15.

2. x/2 + 3 - x/4 < 2

First, let's find a common denominator, which is 4:

(2x/4) + (12/4) - (x/4) < 2

Now, combine the fractions on the left side:

(2x - x + 12) / 4 < 2

Simplify further:

(x + 12) / 4 < 2

Now, multiply both sides of the inequality by 4 to isolate x:

x + 12 < 8

Next, subtract 12 from both sides:

x < 8 - 12

x < -4

So, the solution to the second inequality is x < -4.

To summarize:

1. The solution to the first inequality is x ≤ -15.
2. The solution to the second inequality is x < -4.