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6-8 Accelerated 7 Unit 4 Lesson 10

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Unit 1 Unit 2 Unit 3 •Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 •Lesson 10 Lesson 11 Lesson 12

K-5
6-8
9-12

Accelerated 6
Accelerated 7

Grade 6
Grade 7
Grade 8

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12

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Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 4, Lesson 10

All, Some, or No Solutions

Accelerated 7

Practice

Problem 1

For each equation, decide if it is always true or never true.

\(x - 13 = x + 1\)
\(x+\frac{1}{2} = x - \frac{1}{2}\)
\(2(x + 3) = 5x + 6 - 3x\)
\(x - 3 = 2x - 3 -x\)
\(3(x-5) = 2(x-5) + x\)

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Problem 2

Lesson 10 Resources

Student Materials

Mai says that the equation \(2x + 2 = x +1\) has no solution because the left hand side is double the right hand side. Do you agree with Mai? Explain your reasoning.

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Problem 3

Write the other side of this equation so it's true for all values of \(x\):

\(\frac12(6x-10) - x =\)
Write the other side of this equation so it's true for no values of \(x\):

\(\frac12(6x-10) - x = \)

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Problem 4

Here is an equation that is true for all values of \(x\): \(5(x+2) = 5x+10\).

Elena saw this equation and says she can tell that \(20(x+2)+31=4(5x+10)+31\) is also true for any value of \(x\).

How can she tell? Explain your reasoning.

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Problem 5

ForLesson 7: More Balanced Moves

Elena and Lin are trying to solve \(\frac12x+3=\frac72x+5\). Describe the change they each make to each side of the equation.

Elena’s first step is to write
\(3=\frac72x-\frac12x+5\).

Lin’s first step is to write
\(x+6=7x+10\).

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Problem 6

ForLesson 9: Strategic Solving

Solve each equation and check your solution.

\(3x-6=4(2-3x)-8x\)

\(\frac12z+6=\frac32(z+6)\)

\(9-7w=8w+8\)

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Problem 7

ForLesson 17: Drawing Triangles (Part 2)

A triangle has one side that is 5 units long and an adjacent angle that measures \(25^\circ\). The two other angles in the triangle measure \(90^\circ\) and \(65^\circ\). Complete the two diagrams to create two different triangles with these measurements.

Two images, each a segment with side 5 and a dotted line rising at a 25 degree angle from the segment.

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