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Is the value of [tex]\(2x + 1\)[/tex] twenty greater than [tex]\(8x + 5\)[/tex]?

Sagot :

GinnyAnswer
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].
Hi1315

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

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