Math 60: Notation For Math Problem Solutions.pdf

Evaluating an expression means you have an expression (there is no equal sign in the statement of what you are asked to do). You will often times see the word “evaluate,” “state,” or “find.” Show your substitution step and then work out the arithmetic using equal signs before each line to show equivalency of the expressions. Evaluate 2x2 + 5x −3 for x = −2. If x = −2 then 2x2 + 5x −3 = 2(−2)2 + 5(−2) −3 = 2(4) −10 −3 = 8 −10 −3 = −5.

Checking to see if a number is a solution to an equation in one variable means you have a solution to an equation or inequality is a number which, when plugged into the equation or inequality for the variable, allows for a true statement. Show your substitution into the equation, working both sides simultaneously, and then state whether the number being tested is or is not a solution. Check 2x + 5 = 3x −4 for x = 9. 2(9) + 5 = 3(9) −4 = 18 + 5 = 23 = 23. Is a true statement. So 9 is a solution to the equation.

Solving an equation means you be given an equal sign between two algebraic expressions. You will often times see the word “solve” in the directions. Show your work with your equal signs lined up in the middle of each equation. Do not put equal signs on the left. State what the solution is in a sentence and use either set builder or interval notation as asked for in the directions. Solve 2x + 6 = 5x for x. 2x + 6 = 5x, 2x + 6 −2x = 5x −2x, 6 = 3x, 6/3 = 3x/3, 2 = x. So the solution is 2 and the solution set is {2}.

Determining the horizontal and vertical (often x and y) intercepts means your book may only provide the x or y values. Please follow the directions found on this sheet instead of matching the answers in your book. You will often times see the instructions “find the intercepts.” State the full ordered pairs for all intercepts using a complete sentence. Find the intercepts of 2x −3y = 6. 2x −3(0) = 6, 2x = 6, 2x/2 = 6/2, x = 3, 2(0) −3y = 6, −3y = 6, −3y/−3 = 6/−3, y = −2. The x-intercept is (3, 0) and the y-intercept is (0, −2).

Solving word problems means these problems will generally describe a situation and a relationship between two variables with units defined for each variable. Write your answer as a complete sentence, giving a contextual conclusion which answers the question being asked. If a rock falls from a height of 20 meters on Earth, the height H, in meters, x seconds after it began to fall is approximately H = 20 −4.9x2. What is the height of the rock 1 second after beginning its fall? H = 20 −4.9(1)2, H = 20 −4.9, H = 15.1. The height of the rock 1 second after beginning its fall is approximately 15.1 meters.

Graphing the equation y = 2x −3 means remember, the graph is a picture of the solutions to the equation. The horizontal-axis (often the x-axis) and vertical-axis (often the y axis) are the coordinate system or coordinate plane which we draw the graph onto. Label your horizontal and vertical axes (often x and y) with an appropriate scale, label the line with its equation and any points required by your instructor (often the vertical intercept and sometimes others). Graph the equation y = 2x −3. The slope is m = 2 1 and the y-intercept is (0, −3).