Questionוור 13 Beth says that the equation x + 3 = 5 has only one solution. Is Beth correct? Use the number line to help explain your reasoning. 0 + 2 3 4 95 +4 13 + 16 6 7 8 9 10 same quantity Lesson 22: Solving Equations 213 Suner Teacher

Studdy Solution

STEP 1

1. The equation given is $x + 3 = 5$ .
2. We need to determine if this equation has only one solution.
3. A number line can be used to help explain the reasoning.

STEP 2

1. Solve the equation algebraically.
2. Verify the solution using a number line.
3. Conclude whether Beth is correct.

STEP 3

To solve the equation $x + 3 = 5$ , we need to isolate $x$ .
Subtract 3 from both sides of the equation: $x + 3 - 3 = 5 - 3$
This simplifies to: $x = 2$

STEP 4

Verify the solution using a number line.
Locate the number 2 on the number line. Since the equation $x + 3 = 5$ simplifies to $x = 2$ , the number 2 is the point on the number line that satisfies the equation.

STEP 5

Since the algebraic solution $x = 2$ is verified by the number line, and there are no other values of $x$ that satisfy the equation, Beth is correct in saying that the equation $x + 3 = 5$ has only one solution.
Beth is correct. The equation $x + 3 = 5$ has only one solution: $x = 2$ .

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