Solving Linear Equations and Inequalities
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Questions and Answers

What is the solution for 3x + 5x - 2 = 22?

x = 3

What is the solution for 3x + 1 = 4x - 7?

x = 8

What is the solution for -3x - 4 = 14?

x = -6

What is the solution for -3x + 3 = 4x - 11?

<p>x = 2</p> Signup and view all the answers

What is the solution for x - 3x + 5 = 4x + 11?

<p>x = -1</p> Signup and view all the answers

What is the solution for 4x + 5 = 2x + 23?

<p>x = 9</p> Signup and view all the answers

What is the solution for x + 3x - 4 = 3x - 6?

<p>x = -2</p> Signup and view all the answers

What is the solution for 6x + 5 = 9x + 26?

<p>x = -7</p> Signup and view all the answers

What is the solution for 14 = 3x - 2x + 4x - 11?

<p>x = 5</p> Signup and view all the answers

Which of these numbers are possible values for x? Write commas in between the numbers.

<p>-7</p> Signup and view all the answers

Which letter graph does this linear inequality represent? (Write letter as a) or b) etc.)

<p>c)</p> Signup and view all the answers

Which letter graph does this linear inequality represent? (Write letter as a) or b) etc.)

<p>b)</p> Signup and view all the answers

What is the solution for t?

<p>t ≤ -5</p> Signup and view all the answers

What is the solution for t (leave as a fraction)?

<p>t ≤ 9/8</p> Signup and view all the answers

What is the solution for b?

<p>b ≤ 5</p> Signup and view all the answers

What is the solution for c?

<p>c &gt; -13</p> Signup and view all the answers

Write graph number as 1), 2) etc.

<ol> <li></li> </ol> Signup and view all the answers

Write answer as (1) or (2) etc.

<p>(4)</p> Signup and view all the answers

What is the solution for g: 2g + 4.5 > 8.5?

<p>g &gt; 2</p> Signup and view all the answers

What is the solution for x: 6(8x - 14) < 12?

<p>x &lt; 2</p> Signup and view all the answers

Is 4 a possible answer for x: 2x > 8?

<p>False</p> Signup and view all the answers

Write an inequality: The sum of a number and 9 is less than 22.

<p>x + 9 &lt; 22</p> Signup and view all the answers

Write an inequality: Two times a number is subtracted from 7. The difference is greater than 85.

<p>7 - 2x &gt; 85</p> Signup and view all the answers

Which equation has no solution? (Select the correct equation)

<p>5(x + 3) + x = 4(x + 3) + 3</p> Signup and view all the answers

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?

<p>5</p> Signup and view all the answers

What is the solution for x: 6(x - 1) = 9(x + 2)?

<p>x = -8</p> Signup and view all the answers

How many solutions exist for the given equation: 12x + 1 = 3(4x + 1) - 2?

<p>infinitely many</p> Signup and view all the answers

What is Jillana's best interpretation of the equation that has no solution?

<p>The equation has no solution.</p> Signup and view all the answers

How many solutions exist for the given equation: (x + 12) = 4x - 1?

<p>one</p> Signup and view all the answers

What is the solution for x in the equation 9(x + 1) = 25 + x?

<p>x = 2</p> Signup and view all the answers

What is the value of n in the equation (n - 4) - 3 = 3 - (2n + 3)?

<p>n = 2</p> Signup and view all the answers

What is Jillana's best interpretation if the equation has infinite solutions?

<p>The equation has infinite solutions.</p> Signup and view all the answers

How many solutions exist for the given equation: 3x + 13 = 3(x + 6) + 1?

<p>zero</p> Signup and view all the answers

Study Notes

Solving Linear Equations and Inequalities

  • To solve equations, isolate the variable (x) on one side of the equation.
  • The solution to the equation 3x + 5x - 2 = 22 is x = 3.
  • Simplify equations by collecting like terms and moving constants to one side.

Specific Problems and Solutions

  • For the equation 3x + 1 = 4x - 7, the solution is x = 8.
  • The equation -3x - 4 = 14 solves to x = -6.
  • The solution to -3x + 3 = 4x - 11 is x = 2.
  • The equation x - 3x + 5 = 4x + 11 results in x = -1.
  • Solve 4x + 5 = 2x + 23 to find x = 9.
  • The solution for x + 3x - 4 = 3x - 6 is x = -2.
  • The equation 6x + 5 = 9x + 26 results in x = -7.
  • Solve 14 = 3x - 2x + 4x - 11 to find x = 5.

Inequalities and Their Solutions

  • An inequality describes a relationship between numbers that are not equal.
  • For t, the solution t ≤ -5 indicates all values less than or equal to -5.
  • The fraction result of t ≤ 9/8 indicates values less than or equal to 1.125.
  • The inequality b ≤ 5 means values of b are equal to or less than 5.
  • Solve c > -13, indicating c can be any value greater than -13.
  • g > 2 indicates g must be more than 2.
  • The inequality 2x > 8 shows 4 is not a valid solution for x.

Writing Inequalities

  • The inequality x + 9 < 22 represents the sum of a number and 9 being less than 22.
  • Two times a number subtracted from 7 is represented by 7 - 2x > 85.

Equations with No Solutions

  • The equation 12x + 1 = 3(4x + 1) - 2 has infinitely many solutions.
  • The equation 4(x - 1) - x = 3(x + 5) - 11 reveals no solution when simplified showing similar expressions on both sides.

Types and Number of Solutions

  • Equations can have one, zero, or infinitely many solutions based on their structure.
  • Equations resulting in a variable equal to itself signify infinite solutions.

Example Values and Results

  • For 9(x + 1) = 25 + x, the solution is x = 2.
  • The value in the equation (n - 4) - 3 = 3 - (2n + 3) gives n = 2.

Understanding Graph Representations

  • Various problems require identifying graphs from lettered options that represent linear inequalities.

Decision Making in Solutions

  • Identify whether solutions exist for given equations by recognizing conditions that result in contradictions or confirmations of values.

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Description

This quiz covers the methods for solving linear equations and inequalities. You'll encounter various problems including isolating variables, simplifying equations, and understanding inequalities. Test your knowledge with specific examples and solutions to enhance your skills.

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