Answer :
To determine if the value of \(2x + 1\) is twenty greater than \(8x + 5\), we need to set up the equation reflecting this condition and solve for \(x\). Let's go through the step-by-step solution:
1. Set up the equation:
According to the problem, we need \(2x + 1\) to be twenty greater than \(8x + 5\). Let's write that as an equation:
[tex]\[ 2x + 1 = 8x + 5 + 20 \][/tex]
2. Simplify the equation:
Combine like terms on the right side:
[tex]\[ 2x + 1 = 8x + 25 \][/tex]
3. Isolate the \(x\) terms:
Move the \(x\) terms to one side by subtracting \(8x\) from both sides:
[tex]\[ 2x - 8x + 1 = 25 \][/tex]
Simplify:
[tex]\[ -6x + 1 = 25 \][/tex]
4. Isolate the constant term:
Subtract 1 from both sides to move the constant to the right side:
[tex]\[ -6x = 25 - 1 \][/tex]
Simplify:
[tex]\[ -6x = 24 \][/tex]
5. Solve for \(x\):
Divide both sides by \(-6\):
[tex]\[ x = \frac{24}{-6} \][/tex]
Simplify:
[tex]\[ x = -4 \][/tex]
Hence, the solution to the problem is [tex]\(x = -4\)[/tex]. Therefore, when [tex]\(x = -4\)[/tex], the value of [tex]\(2x + 1\)[/tex] is indeed twenty greater than the value of [tex]\(8x + 5\)[/tex].
1. Set up the equation:
According to the problem, we need \(2x + 1\) to be twenty greater than \(8x + 5\). Let's write that as an equation:
[tex]\[ 2x + 1 = 8x + 5 + 20 \][/tex]
2. Simplify the equation:
Combine like terms on the right side:
[tex]\[ 2x + 1 = 8x + 25 \][/tex]
3. Isolate the \(x\) terms:
Move the \(x\) terms to one side by subtracting \(8x\) from both sides:
[tex]\[ 2x - 8x + 1 = 25 \][/tex]
Simplify:
[tex]\[ -6x + 1 = 25 \][/tex]
4. Isolate the constant term:
Subtract 1 from both sides to move the constant to the right side:
[tex]\[ -6x = 25 - 1 \][/tex]
Simplify:
[tex]\[ -6x = 24 \][/tex]
5. Solve for \(x\):
Divide both sides by \(-6\):
[tex]\[ x = \frac{24}{-6} \][/tex]
Simplify:
[tex]\[ x = -4 \][/tex]
Hence, the solution to the problem is [tex]\(x = -4\)[/tex]. Therefore, when [tex]\(x = -4\)[/tex], the value of [tex]\(2x + 1\)[/tex] is indeed twenty greater than the value of [tex]\(8x + 5\)[/tex].
Answer:
x = -4
Step-by-step explanation:
To determine if 2x + 1 is twenty greater than 8x + 5, we can set up the equation:
2x + 1 = 8x + 5 + 20
Simplify the right side of the equation:
2x + 1 = 8x + 25
Now, solve for x:
Subtract 2x from both sides:
1 = 6x + 25
Subtract 25 from both sides:
1 - 25 = 6x
-24 = 6x
Divide by 6:
x = -4
