The algebraic equation 5 – 2x = 12 is a linear equation with one variable, x. Solving for x involves isolating x on one side of the equation and simplifying it. The solution to this equation provides the value of x that satisfies the given equation.

To begin the process of solving, consider the equation 5 – 2x = 12. To isolate x, it’s necessary to move the constant term, 5, to the other side of the equation by subtracting 5 from both sides. This gives us: -2x = 7.

Next, divide both sides of the equation by -2 to isolate x on one side. This results in: x = -7/2. Therefore, the solution to the equation 5 – 2x = 12 is x = -7/2.

Simplifying the Equation

To simplify the equation, first, let’s distribute the -2 to the terms inside the parentheses: -2x = -10 + 4.

Now, combine like terms on the right-hand side: -2x = -6.

Finally, divide both sides of the equation by -2 to solve for x: x = 3.

Solving for x

To solve for x, we need to isolate it on one side of the equation.

First, we add 2x to both sides of the equation: 5 – 2x + 2x = 12 + 2x.

The -2x and 2x cancel out, leaving us with: 5 = 12 + 2x.

Next, we subtract 12 from both sides of the equation: 5 – 12 = 12 + 2x – 12.

Simplifying, we get: -7 = 2x.

Finally, we divide both sides of the equation by 2 to solve for x: -7/2 = x.

Checking the Solution

To check the solution, we can plug the value of x back into the original equation.

5 – 2(-7/2) = 12

5 + 7 = 12

12 = 12

Since the equation balances, we can confirm that x = -7/2 is the correct solution.

Section 1: Isolating the Variable

  • Subtract 5 from both sides of the equation: -2x = 7.
  • Divide both sides of the equation by -2: x = -7/2.

Section 2: Using Properties of Equality

  • Add 2x to both sides of the equation: 5 – 2x + 2x = 12 + 2x.
  • Simplify: 5 = 12 + 2x.
  • Subtract 12 from both sides of the equation: 5 – 12 = 12 + 2x – 12.
  • Simplify: -7 = 2x.
  • Divide both sides of the equation by 2: x = -7/2.

Section 3: Checking the Solution

  • Substitute x = -7/2 into the original equation: 5 – 2(-7/2) = 12.
  • Simplify: 5 + 7 = 12.
  • Verify: 12 = 12.

Section 4: Alternative Method (Using Multiplication)

  • Multiply both sides of the equation by -1: -5 + 2x = -12.
  • Simplify: 2x = -7.
  • Divide both sides of the equation by 2: x = -7/2.

Section 5: Solving for x in Rational Form

  • Subtract 5 from both sides of the equation: -2x = 7.
  • Multiply both sides of the equation by -1/2: x = -7/2.

Section 6: Verifying the Solution (Using Substitution)

  • Substitute x = -7/2 into the original equation: 5 – 2(-7/2) = 12.
  • Simplify: 5 + 7 = 12.
  • Verify: 12 = 12.

Section 7: Graphing the Solution

  • Graph the equation y = 5 – 2x using a linear equation graphing tool.
  • The x-intercept of the graph is -7/2, which represents the solution to the equation.

Section 8: Applications of the Solution

  • The solution to 5 – 2x = 12 can be used to solve other equations or inequalities that involve the same variable.
  • For example, if we have the equation 3x + 5 – 2x = 12, we can substitute x = -7/2 to find that the equation is true.

Section 9: Related Equations

  • The equation 5 – 2x = 12 is related to the following equations:
    • 2x – 5 = -12
    • 5 – 2x = 7 + 5
    • x – 5/2 = 6

Section 10: Conclusion

In summary, the equation 5 – 2x = 12 has a solution of x = -7/2. This solution can be found using various algebraic techniques, including isolating the variable, using properties of equality, and checking the solution. The solution can be used to solve other equations and inequalities involving the same variable, and it can also be used to graph the corresponding linear equation.

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