Question 119·Medium·Linear Equations in One Variable
What value of satisfies the equation above?
(Express the answer as an integer)
For linear equations in one variable, first simplify each side: distribute over parentheses and combine like terms. Then use inverse operations to move all x-terms to one side of the equation and all constants to the other. When you have a decimal coefficient like 0.6, either rewrite it as a fraction or multiply both sides of the equation by 10 or 100 to clear decimals, then solve the simpler equation and check your result by quickly plugging it back into the original.
Hints
Start with the parentheses
Look at the term . What operation do you need to apply to get rid of the parentheses?
Combine like terms on each side
After distributing, simplify each side of the equation by combining constants (plain numbers) before moving terms across the equal sign.
Isolate the x-term
Once you have an equation like , try to move all x-terms to one side and all constant terms to the other side using addition or subtraction.
Deal with the decimal coefficient
When you reach an equation of the form , think about how to solve it: you can either divide both sides by 0.6 or rewrite 0.6 as a fraction to make the arithmetic easier.
Desmos Guide
Enter each side of the equation as a separate expression
In one expression line, type y = 0.6(x - 5) + 8. In a second expression line, type y = 1.2x - 4. This graphs the left and right sides of the equation as two lines.
Find the intersection point
Zoom or pan the graph until you can see where the two lines cross. Tap or click on the intersection point; Desmos will display its coordinates. The x-coordinate of this intersection is the solution to the equation.
Step-by-step Explanation
Distribute and simplify the left side
Start with the equation:
Distribute 0.6 to both terms inside the parentheses:
So the equation becomes:
Combine the constants on the left side, :
Get x-terms on one side and constants on the other
From
subtract from both sides to move all x-terms to the right side:
Simplify the right side: :
Now add 4 to both sides to move the constants to the left side:
Solve for x
You now have:
Rewrite as a fraction:
So the equation is the same as
To solve for , multiply both sides by the reciprocal of , which is :
So the value of that satisfies the equation is .