6.PAR.7.1 Understand Solutions to Equations & Inequalities

Understand Equations/Inequalities and Solutions

​Key Concept:

​A solution of an equation is a value for the variable that makes the equation true. Substitute values from a given set for the variable and evaluate.

​Vocabulary:

​Equation: is a mathematical sentence that uses an equal sign to show that two expressions are equal.

​Solution of an equation: is a value for the variable that makes the equation true.

​

​***Note- An equation is true when either side of the equals sign are equivalent.

Multiple Choice

When is an equation true?

• When x = any number from 1-10.

• When each side to the right and the left of the = have the same value.

• When the side to the left of the = is greater than the side to the right of the =.

• When the side to the left of the = is less than the side to the right of the =.

​Example:

​Jordan received a $15.00 gift card for phone apps. He used $5.50 of that value and wants to buy one more app to use up the balance. Which app should Jordan buy?

​

​Minecraft: $10.50

​2K Basketball: $8.50

​Spotify Premium: $9.50

​Example:

​Jake has a total of 1,190 Pokemon Cards and 5 boxes. He puts an equal number of Pokemon Cards in each box.

​

​a) Which of his three friends, if any, correctly guessed the number of Pokemon Cards, x, Jake has in each box.

​ Friend A- 234, Friend B- 242, Friend c- 240

​

​b) How many Pokemon Cards did Jake place in each box?

Multiple Choice

$$n=54-36;\ n=8$$  

• True

• False

Multiple Choice

What number would make this equation true? x + 2 = 4

• x = 0

• x = 1

• x = 2

• x = 4

Multiple Choice

Which value for x is the correct solution to this equation? 4.9 = 10.9 - x

• x = 15.8

• x = 5.9

• x = 6.0

• x = 6.9

Multiple Choice

tell which given value

49 = 7r so, r= ............

• 6
• 7
• 10
• 5

Multiple Choice

Anthony has a total of y marbles and 4 boxes. He puts 13 marbles in each box and has none left over. Anthony's friends guessed different numbers to determine how many marbles Anthony had. Use the equation $$y\div4=13$$   to determine how many marbles Anthony has in all.

Julianne's Guess 48 marbles

Nikos's Guess 60 marbles

Quincy's Guess 120 marbles

• $$y\ =\ 52$$  

  None of Anthony friends guessed the correct amount of marbles

• $$y=48$$  

  Julianne guessed the correct amount of marbles

• $$y=60$$  

  Nikos guessed the correct amount of marbles

• $$y=120$$  

  Quincy guessed the correct amount of marbles

Multiple Select

Select all the equations that have 9 as a solution

• $$j+8=72$$  

• $$m\times3=27$$  

• $$b+4=13$$  

• $$p-5=4$$  

• $$q\div3=27$$  

Vocabulary

• Equation: A mathematical sentence that contains an equal sign 

• Inequality: A mathematical sentence that contains the symbols >, <, ≥, or ≤

• Solution: the set of all values which, when substituted for unknowns, make an equation true

• Substitution: the process of replacing a variable in an expression with its actual value.

• Solution Set: the set of all values which, when substituted for unknowns, make an inequality true

Solution vs Solution Set

• As you saw in the vocabulary a solution is a number that make an equation true

• Where a solution set is a set of numbers that make an inequality true.

• ** in your future math classes there will be equations that have multiple solutions but for now we are only working with equations with 1 solution

Try It!

The record time for the girls' 50-meter freestyle swimming competition is 24.49 seconds. Camila has been training and wants to break the record. What are some possible times Camila would have to swim to break the current record? (Write at least 3.)

Multiple Select

Select all would make the inequality true:

x>4

• 1

• 5

• -4

• 9

• 15