Let's solve the problem step by step.
1. Define the Variables:
- Let's denote the three consecutive multiples of 2 as [tex]\( x \)[/tex], [tex]\( x+2 \)[/tex], and [tex]\( x+4 \)[/tex].
2. Set Up the Equation:
- According to the problem, their sum is 18.
- Therefore, we can write the equation: [tex]\( x + (x+2) + (x+4) = 18 \)[/tex].
3. Combine Like Terms:
- Simplify the left side of the equation: [tex]\( x + x + 2 + x + 4 = 18 \)[/tex].
- This can be further simplified to: [tex]\( 3x + 6 = 18 \)[/tex].
4. Isolate the Term with [tex]\( x \)[/tex]:
- Subtract 6 from both sides of the equation to isolate the terms with [tex]\( x \)[/tex]:
[tex]\[
3x + 6 - 6 = 18 - 6
\][/tex]
- This simplifies to: [tex]\( 3x = 12 \)[/tex].
5. Solve for [tex]\( x \)[/tex]:
- Divide both sides by 3 to find the value of [tex]\( x \)[/tex]:
[tex]\[
x = \frac{12}{3} = 4
\][/tex]
6. Find the Three Numbers:
- Now that we have [tex]\( x = 4 \)[/tex], we can find the three consecutive multiples of 2:
[tex]\[
\text{First number: } x = 4
\][/tex]
[tex]\[
\text{Second number: } x+2 = 4+2 = 6
\][/tex]
[tex]\[
\text{Third number: } x+4 = 4+4 = 8
\][/tex]
Therefore, the three consecutive multiples of 2 that sum up to 18 are 4, 6, and 8.
