Solve the following linear equations: 3.1 k − 11 = 2, 3.2 −7 − x = −5, 3.3 5m + 4 = 3m − 12, 3.4 5(x − 1)…

Question

Solve the following linear equations: 3.1 k − 11 = 2, 3.2 −7 − x = −5, 3.3 5m + 4 = 3m − 12, 3.4 5(x − 1) = 4(x − 2)

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the given equations: 3.1 Step 1: Add 11 to both sides of the equation. k − 11 = 2; k − 11 + 11 = 2 + 11 Step 2: Simplify to find the value of k. k = 13 The solution is: k = 13 3.2 Step 1: Add 7 to both sides of the equation. −7 − x = −5; −7 − x + 7 = −5 + 7; −x = 2 Step 2: Multiply both sides by −1 to solve for x. (−1)(−x) = (−1)(2); x = −2 The solution is: x = −2 3.3 Step 1: Subtract 3m from both sides of the equation to collect m terms on one side. 5m + 4 = 3m − 12; 5m − 3m + 4 = −12; 2m + 4 = −12 Step 2: Subtract 4 from both sides to isolate the term with m. 2m + 4 − 4 = −12 − 4; 2m = −16 Step 3: Divide by 2 to solve for m. 2m/2 = (−16)/(2); m = −8 The solution is: m = −8 3.4 Step 1: Distribute the numbers outside the parentheses on both sides of the equation. 5(x − 1) = 4(x − 2); 5x − 5 = 4x − 8 Step 2: Subtract 4x from both sides to collect x terms on one side. 5x − 4x − 5 = −8; x − 5 = −8 Step 3: Add 5 to both sides to solve for x. x − 5 + 5 = −8 + 5; x = −3 The solution is: x = −3

Solve the following linear equations: 3.1 k − 11 = 2, 3.2 -7 - x = -5, 3.3 5m + 4 = 3m − 12, 3.4 5(x − 1) = 4(x − 2)

Answers

Step-by-step solution

Part 3.1· 2 steps

Add 11 to both sides of the equation.

Simplify to find the value of $k$ .

Part 3.2· 2 steps
$x = -2$

Add 7 to both sides of the equation.

Multiply both sides by -1 to solve for $x$ .

Part 3.3· 3 steps
$m = -8$

Subtract $3m$ from both sides of the equation to collect $m$ terms on one side.

Subtract 4 from both sides to isolate the term with $m$ .

Divide by 2 to solve for $m$ .

Part 3.4· 3 steps
$x = -3$

Distribute the numbers outside the parentheses on both sides of the equation.

Subtract $4x$ from both sides to collect $x$ terms on one side.

Add 5 to both sides to solve for $x$ .

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More Mathematics Questions

Solve the following linear equations: 3.1 k − 11 = 2, 3.2 -7 - x = -5, 3.3 5m + 4 = 3m − 12, 3.4 5(x − 1) = 4(x − 2)

Answers

Step-by-step solution

Part 3.1· 2 steps

Add 11 to both sides of the equation.

Simplify to find the value of kkk.

Part 3.2· 2 stepsx=−2x = -2x=−2

Add 7 to both sides of the equation.

Multiply both sides by -1 to solve for xxx.

Part 3.3· 3 stepsm=−8m = -8m=−8

Subtract 3m3m3m from both sides of the equation to collect mmm terms on one side.

Subtract 4 from both sides to isolate the term with mmm.

Divide by 2 to solve for mmm.

Part 3.4· 3 stepsx=−3x = -3x=−3