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Look at the equation below. - 10x + 13 + 12x = 5x - 8 Which of the following steps could be used to transform the equation into the form x = a where a is a number, to show that the equation has one solution? Select TWO options that apply. (2 points) Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation. ☐ Subtract 10x from both sides of the equation and then simplify. Add 5x to both sides of the equation and then simplify. Add 8 to both sides of the equation and then simplify. Subtract 13 from both sides of the equation and then simplify.

5 answers

To transform the equation \(-10x + 13 + 12x = 5x - 8\) into the form \(x = a\), we can consider the following two steps:

  1. Combine like terms on the left side: \(-10x + 12x = 2x\), resulting in the equation \(2x + 13 = 5x - 8\).

  2. Subtract 10x from both sides of the equation may not be the best description, but it is effective to isolate \(x\) through simplification. Instead, subtracting 5x from both sides is a more relevant step, as it helps consolidate \(x\) terms.

  3. Add 8 to both sides of the equation to eliminate the constant on the right side, making it easier to isolate \(x\).

Thus, the correct steps to select are:

  1. Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation. (This statement is a bit misleading as you only combine 10x and 12x to get 2x.)
  2. Add 8 to both sides of the equation and then simplify.

However, it is essential to use the appropriate calculations to transition smoothly to \(x = a\). The simplification steps must lead to isolating \(x\) correctly.

Are you suree

Let’s carefully analyze the equation step-by-step and clarify the correct options to reach the solution:

The original equation is: \[ -10x + 13 + 12x = 5x - 8 \]

Let's break this down:

  1. Combine like terms on the left: \[ (-10x + 12x) + 13 = 5x - 8 \implies 2x + 13 = 5x - 8 \]

  2. You can isolate \(x\) by moving \(x\) terms to one side and constant terms to the other.

Now let’s evaluate the options provided:

  1. Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.

    • This would actually introduce an error. The correct combination is \(-10x + 12x = 2x\).

  2. Subtract 10x from both sides of the equation and then simplify.

    • This is not valid because you'd need to subtract 5x from both sides or isolate terms correctly after combining.

  3. Add 5x to both sides of the equation and then simplify.

    • This is a valid step, as it helps isolate \(x\).

  4. Add 8 to both sides of the equation and then simplify.

    • This also is a valid step to help isolate \(x\).

  5. Subtract 13 from both sides of the equation and then simplify.

    • This would also be a valid step after bringing constants together.

Based on this analysis, the best two options to transform the equation efficiently are:

  • Add 5x to both sides of the equation and then simplify.
  • Add 8 to both sides of the equation and then simplify.

These steps would effectively lead to an expression of the form \(x = a\).

I apologize for any confusion in my previous response. Thank you for your patience!

So your positive that’s the answer

Thank you for your patience. Let's clarify the correct steps one more time. The original equation is:

\[ -10x + 13 + 12x = 5x - 8 \]

Steps to Transform the Equation

  1. Combine like terms on the left side: \[ (-10x + 12x) + 13 = 5x - 8 \implies 2x + 13 = 5x - 8 \]

  2. To isolate \(x\), we can:

    • Add 8 to both sides: \[ 2x + 13 + 8 = 5x - 8 + 8 \implies 2x + 21 = 5x \]

    • Subtract \(2x\) from both sides: \[ 21 = 5x - 2x \implies 21 = 3x \]

    • Finally, divide both sides by 3: \[ x = 7 \]

Correct Options

From the provided options, based on the actions taken to isolate \(x\):

  1. Add 8 to both sides of the equation and then simplify.
  2. Add 5x to both sides of the equation and then simplify. (Note: However, a clearer step after combining like terms as shown should be to subtract \(2x\) or \(5x\) which may be interpreted differently).

To directly answer your question and clarify any ambiguity:

  • The most straightforward options to achieve the solution are indeed Add 5x to both sides of the equation and then simplify and Add 8 to both sides of the equation and then simplify.

These steps effectively work towards isolating \(x\) and represent valid transformations of the equation.

If you have any more questions or would like further clarification, feel free to ask!