Question

2(12+x)-4(x-1)=10; l 5-2x l=4;

Answer 1

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Answer 2

Let's solve the two equations step by step:

1. 2(12+x) - 4(x-1) = 10

First, distribute the terms inside the parentheses: 24 + 2x - 4x + 4 = 10

Combine like terms: 2x - 4x + 28 = 10

Combine constants: -2x + 28 = 10

Now, isolate the variable on one side: -2x = 10 - 28 -2x = -18

Finally, solve for x: x = -18 / -2 x = 9

So the solution to the first equation is x = 9.

2. |5 - 2x| = 4

Since there is an absolute value, we have two cases to consider:

Case 1: 5 - 2x = 4 Subtract 5 from both sides: -2x = 4 - 5 -2x = -1 Divide by -2 (and remember to flip the inequality sign when dividing by a negative number): x = -1 / -2 x = 1/2

Case 2: -(5 - 2x) = 4 Distribute the negative sign: -5 + 2x = 4 Add 5 to both sides: 2x = 4 + 5 2x = 9 Divide by 2: x = 9 / 2 x = 4.5

So the solutions to the absolute value equation are x = 1/2 and x = 4.5.

In conclusion, the solutions to the given equations are x = 9, x = 1/2, and x = 4.5.