IM Alg1.2.7 Practice: Explaining Steps for Rewriting Equations

Match each equation on the left with an equivalent equation on the right. Some of the answer choices are not used.

Mai says that equations A and B have the same solution.

[list][size=150][*]Equation A: [math]-3\left(x+7\right)=24[/math][/*][*]Equation B: [math]x+7=-8[/math][/*][/size][/list]Which statement explains why this is true?

Dividing both sides of Equation A by -3 gives [math]x+7=-8[/math]. Subtracting 3 from both sides of Equation A gives [math]x+7=-8[/math]. Adding 3 to both sides of Equation A gives [math]x+7=-8[/math]. Applying the distributive property to Equation A gives [math]x+7=-8[/math].

Here is an equation:

[size=150][math]2x+10=4x+10[/math][/size][br]Is 0 a solution to this equation? Explain or show your reasoning.

Kiran has evaluated 2 equations.

[size=150]Kiran says that a solution to the equation [math]x+4=20[/math] must also be a solution to the equation [math]5\left(x+4\right)=100[/math].[/size][br][br]Write a convincing explanation as to why this is true.

The entrepreneurship club is ordering potted plants for all 36 of its sponsors.

[size=150]One store charges $8.50 for each plant plus a delivery fee of $20. The equation [math]320=x+7.50\left(36\right)[/math] represents the cost of ordering potted plants at a second store.[/size][br][br]What does the [math]x[/math] represent in this situation?

The cost for each potted plant at the second store The delivery fee at the second store The number of sponsors of the entrepreneurship club The total cost of ordering potted plants at the second store

Here is an equation:

Which equation is equivalent to the equation [math]5x+30=45[/math]?

[math]5x=75[/math] [math]5\left(x+6\right)=45[/math] [math]35x=45[/math] [math]5\left(x+30\right)=45[/math]

The environmental science club is printing T-shirts for its 15 members.

[size=150]The printing company charges a certain amount for each shirt plus a setup fee of $20. [/size][br][br]If the T-shirt order costs a total of $162.50, how much does the company charge for each shirt?

The graph shows the relationship between temperature in degrees Celsius and temperature in degrees Fahrenheit.

[list][*]Mark the point [math]A[/math] on the graph that shows the temperature in Celsius when it is 60 degrees Fahrenheit.[/*][*]Mark the point [math]B[/math] on the graph that shows the temperature in Fahrenheit when it is 60 degrees Celsius.[/*][/list]

Water boils at 100 degrees Celsius. Use the graph to approximate the boiling temperature in Fahrenheit, or to confirm it, if you knew what it is.

The equation that converts Fahrenheit to Celsius is [math]C=\frac{5}{9}\left(F-32\right)[/math]. Use it to calculate the temperature in Celsius when it is 60 degrees Fahrenheit. (This answer will be more exact than the point you found in the first part.)

Here is an equation:

[size=150][math]2x-5=15[/math][/size][br][br]Select [b]all [/b]the equations that have the same solution as this equation.

[math]2x=10[/math] [math]15=5-2x[/math] [math]2x=20[/math] [math]4x-10=30[/math] [math]2x-20=0[/math] [math]2\left(x-5\right)=15[/math]

Diego’s age d is 5 more than 2 times his sister’s age s.

[size=150]This situation is represented by the equation [math]d=2s+5[/math].[/size] [br][br]Which equation is equivalent to the equation [math]d=2s+5[/math]?

[math]\frac{d}{2}=s+5[/math] [math]d-5=2s[/math] [math]d=2\left(s+5\right)[/math] [math]d-2=s+5[/math]

IM Alg1.2.7 Practice: Explaining Steps for Rewriting Equations

Match each equation on the left with an equivalent equation on the right. Some of the answer choices are not used.

Mai says that equations A and B have the same solution.

Here is an equation:

Kiran has evaluated 2 equations.

The entrepreneurship club is ordering potted plants for all 36 of its sponsors.

Here is an equation:

The environmental science club is printing T-shirts for its 15 members.

The graph shows the relationship between temperature in degrees Celsius and temperature in degrees Fahrenheit.

Here is an equation:

Diego’s age d is 5 more than 2 times his sister’s age s.

Information: IM Alg1.2.7 Practice: Explaining Steps for Rewriting Equations