Math / Algebra

QuestionSelect the correct answer.
What is the solution to the equation? $\sqrt{x-3}+1=6$ A. 64 B. 46 C. 28 D. 22

Studdy Solution

STEP 1

1. The equation involves a square root, which requires isolating the square root term.
2. We will need to square both sides to eliminate the square root.

STEP 2

1. Isolate the square root term.
2. Eliminate the square root by squaring both sides.
3. Solve for $x$ .
4. Verify the solution.

STEP 3

Subtract 1 from both sides of the equation to isolate the square root term:
$\sqrt{x-3} + 1 = 6$ $\sqrt{x-3} = 6 - 1$ $\sqrt{x-3} = 5$

STEP 4

Square both sides of the equation to eliminate the square root:
$(\sqrt{x-3})^2 = 5^2$ $x - 3 = 25$

STEP 5

Solve for $x$ by adding 3 to both sides:
$x - 3 = 25$ $x = 25 + 3$ $x = 28$

STEP 6

Verify the solution by substituting $x = 28$ back into the original equation:
$\sqrt{28-3} + 1 = 6$ $\sqrt{25} + 1 = 6$ $5 + 1 = 6$ The solution satisfies the original equation.
The correct answer is:
$\boxed{28}$

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QuestionSelect the correct answer.
What is the solution to the equation? $\sqrt{x-3}+1=6$ A. 64 B. 46 C. 28 D. 22

Studdy Solution

STEP 1

1. The equation involves a square root, which requires isolating the square root term.
2. We will need to square both sides to eliminate the square root.

STEP 2

1. Isolate the square root term.
2. Eliminate the square root by squaring both sides.
3. Solve for $x$ .
4. Verify the solution.

STEP 3

Subtract 1 from both sides of the equation to isolate the square root term:
$\sqrt{x-3} + 1 = 6$ $\sqrt{x-3} = 6 - 1$ $\sqrt{x-3} = 5$

STEP 4

Square both sides of the equation to eliminate the square root:
$(\sqrt{x-3})^2 = 5^2$ $x - 3 = 25$

STEP 5

Solve for $x$ by adding 3 to both sides:
$x - 3 = 25$ $x = 25 + 3$ $x = 28$

STEP 6

Verify the solution by substituting $x = 28$ back into the original equation:
$\sqrt{28-3} + 1 = 6$ $\sqrt{25} + 1 = 6$ $5 + 1 = 6$ The solution satisfies the original equation.
The correct answer is:
$\boxed{28}$

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QuestionSelect the correct answer.What is the solution to the equation? x−3+1=6\sqrt{x-3}+1=6x−3​+1=6 A. 64 B. 46 C. 28 D. 22

Studdy Solution

STEP 1

1. The equation involves a square root, which requires isolating the square root term.2. We will need to square both sides to eliminate the square root.

STEP 2

1. Isolate the square root term.2. Eliminate the square root by squaring both sides.3. Solve for x x x.4. Verify the solution.

STEP 3

Subtract 1 from both sides of the equation to isolate the square root term:x−3+1=6\sqrt{x-3} + 1 = 6x−3​+1=6 x−3=6−1\sqrt{x-3} = 6 - 1x−3​=6−1 x−3=5\sqrt{x-3} = 5x−3​=5

STEP 4

Square both sides of the equation to eliminate the square root:(x−3)2=52(\sqrt{x-3})^2 = 5^2(x−3​)2=52 x−3=25x - 3 = 25x−3=25

STEP 5

Solve for x x x by adding 3 to both sides:x−3=25x - 3 = 25x−3=25 x=25+3x = 25 + 3x=25+3 x=28x = 28x=28

STEP 6

Verify the solution by substituting x=28 x = 28 x=28 back into the original equation:28−3+1=6\sqrt{28-3} + 1 = 628−3​+1=6 25+1=6\sqrt{25} + 1 = 625​+1=6 5+1=65 + 1 = 65+1=6 The solution satisfies the original equation. The correct answer is:28 \boxed{28} 28​

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QuestionSelect the correct answer.
What is the solution to the equation? $\sqrt{x-3}+1=6$ A. 64 B. 46 C. 28 D. 22

1. The equation involves a square root, which requires isolating the square root term.
2. We will need to square both sides to eliminate the square root.

1. Isolate the square root term.
2. Eliminate the square root by squaring both sides.
3. Solve for $x$ .
4. Verify the solution.

Subtract 1 from both sides of the equation to isolate the square root term:
$\sqrt{x-3} + 1 = 6$ $\sqrt{x-3} = 6 - 1$ $\sqrt{x-3} = 5$

Square both sides of the equation to eliminate the square root:
$(\sqrt{x-3})^2 = 5^2$ $x - 3 = 25$

Solve for $x$ by adding 3 to both sides:
$x - 3 = 25$ $x = 25 + 3$ $x = 28$

Verify the solution by substituting $x = 28$ back into the original equation:
$\sqrt{28-3} + 1 = 6$ $\sqrt{25} + 1 = 6$ $5 + 1 = 6$ The solution satisfies the original equation.
The correct answer is:
$\boxed{28}$