Question

/2x-3/=4 /2x+30/=48 /5x+6/=7 /9-3x/=6

Answer 1

1)ответ - 3.5 2)ответ - 6 3)овтет - 0.2 4=овтет - 1

Answer 2

To solve each absolute value equation, we need to consider both the positive and negative values of the expression within the absolute value bars. Let's solve each equation one by one:

1. |2x - 3| = 4

To solve for x, we'll set up two cases:

Case 1: 2x - 3 = 4 Add 3 to both sides: 2x = 4 + 3 2x = 7 Divide by 2: x = 7/2

Case 2: -(2x - 3) = 4 Remove the negative sign: -2x + 3 = 4 Subtract 3 from both sides: -2x = 4 - 3 -2x = 1 Divide by -2: x = -1/2

So, the solutions for the equation |2x - 3| = 4 are x = 7/2 and x = -1/2.

2. |2x + 30| = 48

Again, set up two cases:

Case 1: 2x + 30 = 48 Subtract 30 from both sides: 2x = 48 - 30 2x = 18 Divide by 2: x = 18/2 x = 9

Case 2: -(2x + 30) = 48 Remove the negative sign: -2x - 30 = 48 Add 30 to both sides: -2x = 48 + 30 -2x = 78 Divide by -2: x = 78/-2 x = -39

The solutions for the equation |2x + 30| = 48 are x = 9 and x = -39.

3. |5x + 6| = 7

Two cases:

Case 1: 5x + 6 = 7 Subtract 6 from both sides: 5x = 7 - 6 5x = 1 Divide by 5: x = 1/5

Case 2: -(5x + 6) = 7 Remove the negative sign: -5x - 6 = 7 Add 6 to both sides: -5x = 7 + 6 -5x = 13 Divide by -5: x = 13/-5

The solutions for the equation |5x + 6| = 7 are x = 1/5 and x = -13/5.

4. |9 - 3x| = 6

Two cases:

Case 1: 9 - 3x = 6 Subtract 9 from both sides: -3x = 6 - 9 -3x = -3 Divide by -3: x = -3/-3 x = 1

Case 2: -(9 - 3x) = 6 Remove the negative sign: -(-3x + 9) = 6 Distribute the negative sign: 3x - 9 = 6 Add 9 to both sides: 3x = 6 + 9 3x = 15 Divide by 3: x = 15/3 x = 5

The solutions for the equation |9 - 3x| = 6 are x = 1 and x = 5.

So, the solutions for the given absolute value equations are:

x = 7/2 and x = -1/2 (for |2x - 3| = 4) x = 9 and x = -39 (for |2x + 30| = 48) x = 1/5 and x = -13/5 (for |5x + 6| = 7) x = 1 and x = 5 (for |9 - 3x| = 6)