Constructing Equations with One Solution
Constructing Equations with One Solution is a Grade 7 math skill in Reveal Math Accelerated, Unit 8: Solve Problems Using Equations and Inequalities, where students learn the conditions that produce a linear equation with exactly one solution — when the variable coefficient is different on each side — and practice writing and solving such equations. This contrasts with equations that have no solution or infinitely many solutions.
Key Concepts
To construct a linear equation with exactly one solution, ensure that the coefficients of the variable on each side of the equation are different. The constants can be any value.
An equation in the form $ax + b = cx + d$ has exactly one solution if and only if: $$a \neq c$$.
Common Questions
What makes a linear equation have exactly one solution?
A linear equation has exactly one solution when simplifying leads to a statement of the form x = a, which means the variable coefficients on each side are different. There is a unique value of x that satisfies the equation.
How do you construct an equation with one solution?
Write an equation where the coefficient of the variable is different on the left and right sides after simplifying. For example, 3x + 2 = 2x + 7 has one solution because the x coefficients (3 and 2) differ, giving x = 5.
How does an equation with one solution differ from no-solution or infinite-solutions equations?
A no-solution equation simplifies to a false statement like 3 = 5, and an infinite-solutions equation simplifies to a true statement like 0 = 0. A one-solution equation simplifies to x = a specific number.
What is Reveal Math Accelerated Unit 8 about?
Unit 8 covers Solve Problems Using Equations and Inequalities, including solving one- and two-step equations, constructing equations with specific solution types, and solving inequalities.