University:
Jackson College
Course:
MAT-010 | Basic Mathematics
Academic year:

2024
Views:

495

Pages:

2
Author:

Bennett Wheeler

Question 1 Solve for 𝑥 x in the equation 2 𝑥 − 7 = 0.5 𝑥 + 0.5 2x−7=0.5x+0.5. Answer 1 To eliminate decimals, multiply both sides by 10: 10 ( 2 𝑥 − 7 ) = 10 ( 0.5 𝑥 + 0.5 ) 10(2x−7)=10(0.5x+0.5) 20 𝑥 − 70 = 5 𝑥 + 5 20x−70=5x+5 Subtract 5 𝑥 5x from both sides: 15 𝑥 − 70 = 5 15x−70=5 Add 70 to both sides: 15 𝑥 = 75 15x=75 Divide by 15: 𝑥 = 5 x=5 Question 2 Five more than eight times a number is the same as twenty-one less than the number. Answer 1 Let 𝑥 x be the number. Eight times the number: 8 𝑥 8x. Five more than eight times the number: 5 + 8 𝑥 5+8x. Twenty-one less than the number: 𝑥 − 21 x−21. Set up the equation: 5 + 8 𝑥 = 𝑥 − 21 5+8x=x−21 Subtract 𝑥 x from both sides: 7 𝑥 + 5 = − 21 7x+5=−21 Subtract 5 from both sides: 7 𝑥 = − 26 7x=−26 Divide by 7: 𝑥 = − 26 7 x=− 7 26 Question 3 Write the equation in point-slope form of the line that passes through the given point with the given slope. Point: ( 3 , 1 ) (3,1), Slope: 𝑚 = 2 m=2. Answer 1 The point-slope form of a line is: 𝑦 − 𝑦 1 = 𝑚 ( 𝑥 − 𝑥 1 ) y−y 1 =m(x−x 1 ) Substitute 𝑚 = 2 m=2, 𝑥 1 = 3 x 1 =3, and 𝑦 1 = 1 y 1 =1: 𝑦 − 1 = 2 ( 𝑥 − 3 ) y−1=2(x−3) Simplify: 𝑦 − 1 = 2 𝑥 − 6 y−1=2x−6 Thus, the equation is: 𝑦 = 2 𝑥 − 5 y=2x−5 Question 4 Find the y-intercept of the equation 𝑦 = 3 𝑥 − 5 y=3x−5. Answer 1 The y-intercept occurs when 𝑥 = 0 x=0: 𝑦 = 3 ( 0 ) − 5 y=3(0)−5 𝑦 = − 5 y=−5 The y-intercept is − 5 −5. Question 5 A wire 22 cm long is cut into two pieces. The longer piece is 2 cm longer than the shorter piece. Answer 1 Let the length of the shorter piece be 𝑥 x cm. Then, the longer piece is 𝑥 + 2 x+2 cm. The total length of the wire is 22 cm, so: 𝑥 + ( 𝑥 + 2 ) = 22 x+(x+2)=22 Combine terms: 2 𝑥 + 2 = 22 2x+2=22 Subtract 2 from both sides: 2 𝑥 = 20 2x=20 Divide by 2: 𝑥 = 10 x=10 The shorter piece is 10 cm, and the longer piece is 10 + 2 = 12 10+2=12 cm.