Question

1). 2,5х=-1 2). 0,3х=1 3). 7x=-3 4). -16x=8 5). |x|-5=0 6). |x|+3,2=8 7). 4,1-|x|=5 8). |3x+1,8|=0 9). 9|x|-6=0 10). 8/x=6/5

Answer 1

1) -2/5

2)10/3

-3/7

. -1/2

5

4,8

0,9

0,60,6

Answer 2

To solve each equation, we'll isolate the variable "x" on one side of the equation. Let's go through each of them step by step:

1. 2.5x = -1 Divide both sides by 2.5: x = -1 / 2.5 x = -0.4

2. 0.3x = 1 Divide both sides by 0.3: x = 1 / 0.3 x = 10/3 x ≈ 3.33

3. 7x = -3 Divide both sides by 7: x = -3 / 7

4. -16x = 8 Divide both sides by -16: x = 8 / -16 x = -0.5

5. |x| - 5 = 0 Add 5 to both sides: |x| = 5 Since the absolute value of x can be either positive or negative when equal to 5, we have two solutions: x = 5 and x = -5

6. |x| + 3.2 = 8 Subtract 3.2 from both sides: |x| = 8 - 3.2 |x| = 4.8 Since the absolute value of x can be either positive or negative when equal to 4.8, we have two solutions: x = 4.8 and x = -4.8

7. 4.1 - |x| = 5 Subtract 4.1 from both sides:

• |x| = 5 - 4.1
• |x| = 0.9 Now, isolate the absolute value: |x| = -0.9 Since the absolute value can't be negative, there is no real solution to this equation.

8. |3x + 1.8| = 0 The absolute value of any number is non-negative, and the only way it can be equal to 0 is when the expression inside the absolute value is 0: 3x + 1.8 = 0 Subtract 1.8 from both sides: 3x = -1.8 Divide by 3: x = -1.8 / 3 x = -0.6

9. 9|x| - 6 = 0 Add 6 to both sides: 9|x| = 6 Divide by 9: |x| = 6 / 9 |x| = 2/3 Since the absolute value can be either positive or negative when equal to 2/3, we have two solutions: x = 2/3 and x = -2/3

10. 8/x = 6/5 To isolate x, cross-multiply: 8 * 5 = 6 * x 40 = 6x Divide by 6: x = 40 / 6 x ≈ 6.67

Please note that in equations 7 and 9, we ended up with no real solutions because the equations were inconsistent or had extraneous solutions. Always check the validity of solutions in the original equation to ensure they are accurate.