1+5|4x-10|=46 — step-by-step solution | Explain MAths

1+5|4x-10|=46

1) Let's solve in

ℝ

:

1 + 5 \cdot | 4 x - 10 | = 46

ⓘ We subtract

1

from both sides

5 \cdot | 4 x - 10 | = 46 - 1

ⓘ Start from

46

and move back

1

on the number line:

46 - 1

=

45

5 \cdot | 4 x - 10 | = 45

Since

5 \neq 0

, divide both sides by

5

:

| 4 x - 10 | = 9

Since

9 \geq 0

,

| 4 x - 10 | = 9

is equivalent to

4 x - 10 = 9

or

4 x - 10 = -9

2) Let's solve in

ℝ

:

4 x - 10 = 9

ⓘ We add

10

to both sides

4 x = 9 + 10

ⓘ Start from

9

and move forward

10

on the number line:

9 + 10

=

19

4 x = 19

ⓘ Both sides are divided by

4

Solution found:

x = \frac{19}{4}

3) Let's solve in

ℝ

:

4 x - 10 = -9

ⓘ We add

10

to both sides

4 x = - 9 + 10

ⓘ Start from

-9

and move forward

10

on the number line, going past zero:

- 9 + 10

=

1

4 x = 1

ⓘ Both sides are divided by

4

Solution obtained:

x = \frac{1}{4}

▶Solution:

x = {\frac{1}{4}, \frac{19}{4}}

4) The numeric value of:

x = {\frac{1}{4}, \frac{19}{4}}

equals:

▷

x = {0.25, 4.75}