Question

Solve each equation for the given variable. Check your answers by hand or by calculator. a. \(1.04+0.293+x=5.3\) b. \(0.01003-x=0.0091\) c. \(y-7.623=84.212\) d. \(1.626+b=14.503\) e. \(x+8.28=3.4\) f. \(0.0114+z=0.005+0.0101\)

Short answer

Question: Solve the following linear algebraic equations for the given variable. a. 1.04 + 0.293 + x = 5.3 b. 0.01003 - x = 0.0091 c. y - 7.623 = 84.212 d. 1.626 + b = 14.503 e. x + 8.28 = 3.4 f. 0.0114 + z = 0.005 + 0.0101 Answer: a. x = 3.967 b. x = 0.00093 c. y = 91.835 d. b = 12.877 e. x = -4.88 f. z = 0.0037

Step-by-step solution

Combine like terms

Add \(1.04\) and \(0.293\) together to get \(1.333\). So, the equation becomes, \(1.333 + x = 5.3\).

Isolate x

To isolate x, subtract \(1.333\) from both sides of the equation: \(x = 5.3 - 1.333\).

Solve for x

When you subtract \(1.333\) from \(5.3\), you get \(x = 3.967\). #b. 0.01003 - x = 0.0091#

Add x to both sides

Add x to both sides of the equation to isolate x on the left side: \(0.01003 = 0.0091 + x\).

Solve for x

Subtract \(0.0091\) from \(0.01003\) to find the value of x: \(x = 0.01003 - 0.0091 = 0.00093\). #c. y - 7.623 = 84.212#

Add 7.623 to both sides

Add \(7.623\) to both sides of the equation to isolate y: \(y = 84.212 + 7.623\).

Solve for y

Add \(84.212\) and \(7.623\) together to find the value of y: \(y = 91.835\). #d. 1.626 + b = 14.503#

Subtract 1.626 from both sides

Subtract \(1.626\) from both sides of the equation to isolate b: \(b = 14.503 - 1.626\).

Solve for b

Subtract \(1.626\) from \(14.503\) to find the value of b: \(b = 12.877\). #e. x + 8.28 = 3.4#

Subtract 8.28 from both sides

Subtract \(8.28\) from both sides of the equation to isolate x: \(x = 3.4 - 8.28\).

Solve for x

Subtract \(8.28\) from \(3.4\) to find the value of x: \(x = -4.88\). #f. 0.0114 + z = 0.005 + 0.0101#

Combine like terms

Add \(0.005\) and \(0.0101\) together to get \(0.0151\). So, the equation becomes, \(0.0114 + z = 0.0151\).

Subtract 0.0114 from both sides

Subtract \(0.0114\) from both sides to isolate z: \(z = 0.0151 - 0.0114\).

Solve for z

Subtract \(0.0114\) from \(0.0151\) to find the value of z: \(z = 0.0037\).