What does it mean to solve a problem algebraically?

To solve a problem algebraically means to find the solution to a mathematical problem by using algebraic methods, such as manipulating equations, expressions, and using algebraic rules and properties. In algebra, this involves steps like simplifying expressions, isolating variables, applying operations like addition, subtraction, multiplication, or division, and using algebraic identities or formulas.

For example, if you are given an equation like 2x + 3 = 7, solving it algebraically involves the following steps:

Isolate the variable (x): Start by getting x alone on one side of the equation.

Subtract 3 from both sides:
2x = 7 - 3
2x = 4
Solve for x: Now, divide both sides of the equation by 2 to find x.

Divide both sides by 2:
x = 4 ÷ 2
x = 2
Thus, the algebraic solution to the equation is x = 2.

In essence, solving algebraically means using algebraic tools and methods to transform a given problem into a simpler form, often leading to the discovery of unknown variables or values.