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Which equation is equivalent to 4x +3 + (-3x) + 7х- 6x = 11?

A. 8x + 3 = 11
B. 2x + 3 = 11
C. 5х= 11
• D. —4х = 11

11 answers

Let's simplify the equation step by step:

Starting with: \[ 4x + 3 + (-3x) + 7x - 6x = 11 \]

Combine like terms (the terms with \(x\)):

  1. Combine \(4x\), \(-3x\), \(7x\), and \(-6x\): \[ (4x - 3x + 7x - 6x) = (4 - 3 + 7 - 6)x = 2x \]

  2. Now the equation becomes: \[ 2x + 3 = 11 \]

Therefore, the equivalent equation is: \[ 2x + 3 = 11 \]

So the correct option is B. 2x + 3 = 11.

Select the expression equivalent to (-13x - 15) - (-9x + 16).
A. 4x — 31
В.
-4x+1
• с.-4х - 31
• D. -22х - 31

To simplify the expression \((-13x - 15) - (-9x + 16)\), we can follow these steps:

  1. Distribute the negative sign to the terms inside the parentheses: \[ -13x - 15 + 9x - 16 \]

  2. Combine like terms:

    • For the \(x\) terms: \(-13x + 9x = -4x\)
    • For the constant terms: \(-15 - 16 = -31\)

So, combining everything gives us: \[ -4x - 31 \]

Therefore, the equivalent expression is: \(-4x - 31\)

So the correct option is C. -4x - 31.

Stephanie sells 12 pretzels per hour. Robert sells 15 pretzels per hour. This week, Robert sold an additional 18 pretzels. Which of the following expressions represents the total sales of both people this week, where S represents the number of hours that Stephanie worked and R represents the number of hours that Robert worked?
• A. 12S + 15R + 18
• B. 155 + 12R + 18
C. 125 + 18R
D. 12S + 15R

To find the total sales of both Stephanie and Robert this week, we can break down their sales based on the information provided:

  1. Stephanie's sales: She sells 12 pretzels per hour, so if she worked \(S\) hours, her total sales would be \(12S\).

  2. Robert's sales: He sells 15 pretzels per hour. If he worked \(R\) hours, his total sales from those hours would be \(15R\). Additionally, we know he sold an extra 18 pretzels this week.

Putting it all together, the total sales for both Stephanie and Robert can be represented by the following expression: \[ 12S + 15R + 18 \]

Thus, the correct option is A. 12S + 15R + 18.

Which of the following is a simplified version of 12 - 2(x + 1) = 5?
• А. -2x + 10 = 5
B. —2x + 13 = 5
C. 10x + 1 = 5
• D. 10x + 10 = 5

To simplify the equation \( 12 - 2(x + 1) = 5 \), let's follow the steps:

  1. Distribute \(-2\) into \((x + 1)\): \[ 12 - 2x - 2 = 5 \]

  2. Combine like terms on the left side: \[ 12 - 2 = 10 \] So, the equation simplifies to: \[ 10 - 2x = 5 \]

Thus, we have: \[ -2x + 10 = 5 \]

Therefore, the simplified version of the equation is: A. \(-2x + 10 = 5\).

Which equation is equivalent to 3 + 5(x + 2) = 12?
• A. 8x + 16 = 12
• • B. 8x + 2 = 12
C. 5x + 5 = 12
• • D. 5x + 13 = 12

To find an equation equivalent to \(3 + 5(x + 2) = 12\), we'll simplify the left side step by step.

  1. Start by distributing the \(5\) into \((x + 2)\): \[ 3 + 5x + 10 = 12 \]

  2. Combine the constant terms \(3\) and \(10\): \[ (3 + 10) + 5x = 12 \implies 13 + 5x = 12 \]

So the equation can be rewritten as: \[ 5x + 13 = 12 \]

Therefore, the equivalent equation is: D. \(5x + 13 = 12\).

Kayla is purchasing 5 candles for x dollars each and 5 candle holders for $3.50 each. Kayla paid a total of $27.50. Before tax, what is the cost per candle?

• A. $2.00

• В. $4.80

• C. $6.20

• D. $9.00

To determine the cost per candle, we can set up an equation based on the information given.

  1. Total cost of candles: Kayla is purchasing 5 candles for \( x \) dollars each, so the total cost for the candles is: \[ 5x \]

  2. Total cost of candle holders: She is purchasing 5 candle holders for $3.50 each, so the total cost for the candle holders is: \[ 5 \times 3.50 = 17.50 \]

  3. Total cost paid: Kayla paid a total of $27.50. Therefore, we can set up the following equation: \[ 5x + 17.50 = 27.50 \]

  4. Solving for \( x \): Subtract \( 17.50 \) from both sides: \[ 5x = 27.50 - 17.50 \] \[ 5x = 10.00 \] Now, divide both sides by 5: \[ x = \frac{10.00}{5} = 2.00 \]

Thus, the cost per candle before tax is A. $2.00.