High School

Select all the following values of [tex] m [/tex] that are solutions to the equation:

1. [tex] -1 = 4m + 19 [/tex]
2. [tex] -5 [/tex]
3. [tex] 4m + 19 = -14m [/tex]
4. [tex] -19 - \frac{18}{20}m = 0 [/tex]
5. [tex] -1 [/tex]

Answer :

Let's solve the given equation step-by-step to find the values of [tex]\( m \)[/tex] that satisfy it.

The equation given is:
[tex]\[
-1 = 4m + 19
\][/tex]

1. Isolate the term with [tex]\( m \)[/tex]:

We need to get the term involving [tex]\( m \)[/tex] by itself. To do this, subtract 19 from both sides of the equation:
[tex]\[
-1 - 19 = 4m
\][/tex]
Simplifying the left side gives:
[tex]\[
-20 = 4m
\][/tex]

2. Solve for [tex]\( m \)[/tex]:

To find [tex]\( m \)[/tex], divide both sides by 4:
[tex]\[
m = \frac{-20}{4}
\][/tex]
Simplifying the right side gives:
[tex]\[
m = -5
\][/tex]

Now, let's check which of the options given might be solutions. You mentioned one option: [tex]\(-5\)[/tex].

- Verify the solution:

Substitute [tex]\( m = -5 \)[/tex] back into the original equation to verify it satisfies the equation:
[tex]\[
-1 = 4(-5) + 19
\][/tex]
This simplifies to:
[tex]\[
-1 = -20 + 19
\][/tex]
[tex]\[
-1 = -1
\][/tex]
The equation holds true.

Thus, the value [tex]\( m = -5 \)[/tex] is indeed a solution to the equation.