Question

1). 7х+2/6-х≤5х+4/3-4х. 2). 4х+1/3-х+1/2-х-3/4

Answer 1

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Answer 2

To solve the inequalities, let's begin with the first one:

1. 7x + 2/6 - x ≤ 5x + 4/3 - 4x

Step 1: Combine the "x" terms on the left-hand side and the constant terms on the right-hand side:

7x - x + 2/6 ≤ 5x - 4x + 4/3

Simplify the equation:

6x + 1/3 ≤ x + 4/3

Step 2: Move all the "x" terms to the left-hand side and constant terms to the right-hand side by subtracting x and 1/3 from both sides:

6x - x ≤ 4/3 - 1/3

Simplify:

5x ≤ 1

Step 3: Finally, solve for x by dividing both sides by 5:

x ≤ 1/5

So the solution for the first inequality is x ≤ 1/5.

Now, let's move on to the second inequality:

2. 4x + 1/3 - x + 1/2 - x - 3/4

To solve this, we need to combine the "x" terms and the constant terms:

4x - x - x + 1/3 + 1/2 - 3/4

Combine the "x" terms:

2x + 1/3 + 1/2 - 3/4

Step 1: Find a common denominator for the fractions (24 is the least common multiple of 3, 2, and 4):

(2x * 24) + (1 * 8) + (1 * 12) - (3 * 6) / 24

Simplify:

48x + 8 + 12 - 18 / 24

Step 2: Combine the constant terms:

48x + 2 / 24

Step 3: Simplify further:

48x + 1/12

So the simplified inequality is 48x + 1/12. There's no comparison or inequality sign in the given expression, so we can't solve it as an inequality without additional information. If there's a comparison symbol (like ≤, ≥, <, >, etc.) provided, we can proceed to solve the inequality accordingly.