Question $3 x-21=2 x+$

Studdy Solution

STEP 1

1. The equation $3x - 21 = 2x + \_$ is missing a constant term on the right side.
2. We need to solve for $x$ assuming the missing term is a constant.
3. The equation involves basic algebraic operations, specifically addition and subtraction.

STEP 2

1. Identify the missing term.
2. Isolate the variable $x$ by performing algebraic operations.
3. Verify the solution by substituting it back into the equation.

STEP 3

Assume the missing term is a constant, say $c$ . Rewrite the equation as:
$3x - 21 = 2x + c$

STEP 4

Subtract $2x$ from both sides to start isolating $x$ :
$3x - 2x - 21 = c$
Simplify the left side:
$x - 21 = c$

STEP 5

Add 21 to both sides to solve for $x$ :
$x = c + 21$

STEP 6

To verify, substitute $x = c + 21$ back into the original equation:
$3(c + 21) - 21 = 2(c + 21) + c$
Simplify both sides to check if they are equal:
$3c + 63 - 21 = 2c + 42 + c$
$3c + 42 = 3c + 42$
Both sides are equal, confirming the solution is consistent.
The solution in terms of the constant $c$ is:
$x = c + 21$

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