Sure, let's solve the equation step-by-step.
Given equation:
[tex]\[ -2(2x - 5) - 18 = 0 \][/tex]
First, distribute the -2 across the parentheses:
[tex]\[ -2 \cdot 2x - (-2 \cdot 5) - 18 = 0 \][/tex]
This simplifies to:
[tex]\[ -4x + 10 - 18 = 0 \][/tex]
Combine the constants:
[tex]\[ -4x - 8 = 0 \][/tex]
Next, isolate [tex]\( x \)[/tex] by adding 8 to both sides:
[tex]\[ -4x = 8 \][/tex]
Then, divide both sides by -4:
[tex]\[ x = -2 \][/tex]
So, the value of [tex]\( x \)[/tex] is:
[tex]\[ x = -2 \][/tex]
Now, let's find the value when [tex]\( b = 3 \)[/tex]. Here, interpret the equation [tex]\( -2(2x - 5) - 18 = 0 \)[/tex] in terms of [tex]\( b \)[/tex]:
First, substitute [tex]\( b = 3 \)[/tex] into the equation. This yields:
[tex]\[ -2(2 \cdot 3 - 5) - 18 \][/tex]
Calculate inside the parentheses first:
[tex]\[ 2 \cdot 3 = 6 \][/tex]
[tex]\[ 6 - 5 = 1 \][/tex]
Now, replace the simplified terms back into the equation:
[tex]\[ -2 \cdot 1 - 18 \][/tex]
Multiply:
[tex]\[ -2 \cdot 1 = -2 \][/tex]
Finally,
[tex]\[ -2 - 18 = -20 \][/tex]
Now, negating -20, we have:
[tex]\[ 20 \][/tex]
So, when [tex]\( b = 3 \)[/tex]:
[tex]\[ x = 20 \][/tex]
Thus, the complete answers are:
- The value of [tex]\( x \)[/tex] is [tex]\( -2 \)[/tex].
- The value of [tex]\( x \)[/tex] when [tex]\( b = 3 \)[/tex] is [tex]\( 20 \)[/tex].
