Question

1)0,5×|2x-5|=1,5 2)6,8×|5x-24|=1,7​

Answer 1

0,5 * |2x - 5| = 1,5

|2x - 5| = 3

2x - 5 = 3; 2x - 5 = - 3

$x_{1} = 1; x_{2} = 4$

6,8 * |5x - 24| = 1,7

|5x - 24| = 0,25

5x - 24 = 0,25; 5x - 24 = - 0,25

$x_{1} = 4,75; x_{2} = 4,85$

Answer 2

To solve the equations $0.5 \cdot |2x - 5| = 1.5$ and $6.8 \cdot |5x - 24| = 1.7$, we'll follow these steps:

1. Solve $0.5 \cdot |2x - 5| = 1.5$:

First, divide both sides by 0.5 to isolate the absolute value:

$|2x - 5| = 3$

This gives two possible equations:

a) $2x - 5 = 3$ b) $2x - 5 = -3$

Solve for $x$ in each equation:

a) $2x = 8$ => $x = 4$

b) $2x = 2$ => $x = 1$

So, the solutions for the first equation are $x = 4$ and $x = 1$.

2. Solve $6.8 \cdot |5x - 24| = 1.7$:

First, divide both sides by 6.8:

$|5x - 24| = 0.25$

This gives two possible equations:

a) $5x - 24 = 0.25$ b) $5x - 24 = -0.25$

Solve for $x$ in each equation:

a) $5x = 24.25$ => $x \approx 4.85$

b) $5x = 23.75$ => $x \approx 4.75$

So, the solutions for the second equation are $x \approx 4.85$ and $x \approx 4.75$.