Tutor profile: Avi S.
Solve for x: 4x + 6 * 2 - 8 = 2x + 4 * 3 + 6
Whenever solving an equation for x, the easiest method is to group all the x variable terms on one side of the equation and group all the constant numbers on the other side of the equation. For this question, we have to use order of operations (PEMDAS) to solve for the constant numbers on each side of the equation. Looking at the left side: 4x + 6 * 2 - 8, we first multiply (6 * 2) = 12 and then subtract 8, getting 12 - 8 = 4. Don't forget about the 4x though :) Our simplified left side of the equation will be 4x + 4. Now looking at the right side of the equation, we first multiply (4 * 3) = 12 and then add 6, getting 12 + 6 = 18. Our simplified right side of the equation will be 2x + 18. Putting the left and right sides of the equation together, we get 4x + 4 = 2x + 18. From here, we can get the x variables on the left side of the equation and the constant terms on the right side. To do this, we subtract 2x from the right side (remember that we always have to do this on both sides of the equation), meaning we have to also subtract 2x from the left side. Similarly, we subtract 4 from both the left and right sides. We end up with 2x = 14. Now, we can divide both sides of the equation by 2: getting x = 7.
Subject: Basic Math
Bob goes out to dinner with a few friends and is tasked with paying the tip for the table. The group orders 2 burgers (each costing $7.99) , 2 pizzas (each costing $11.78), and 4 lemonades (each costing $2.49). They decide to give a 20% tip to the waiter. How much does Bob have to pay for the tip?
Looking at the problem, we can determine that this is a percentage problem with some addition and multiplication elements sprinkled in. In order to calculate the percentage tip, one must first calculate the total cost of all the food, and then determine 20% of that value to figure out the tip amount. Calculations for the total cost of the food: (2 x 7.99) + (2 x 11.78) + (4 x 2.49) = $15.98 + $23.56 + $9.96 = $49.5. $49.5 is the total cost for all the food. Now, we must determine 20% of $49.5 to figure out the amount Bob has to tip. 20% of something is equivalent to 1/5 of something because 20/100 = 1/5. We can use this to make the problem easier by dividing 49.5 by 5. Doing this we get $9.9. So, the amount Bob has to pay for the tip is $9.9.
Find the number of solutions to the following system of equations: -6x + 4y = 2 3x - 2y = -1
Whenever approaching a system of equations problem, one should decide on using either the elimination or substitution approach. In this case, eliminating the x variable can easily be done by multiplying the second equation by -2. An important step to remember is that the entire equation is being multiplied by -2 and not just the x variable (this is a common mistake students can make). Once the 2nd equation is multiplied by -2, the system will look like this: -6x + 4y = 2 -6x + 4y = 2 When solving a system of equations problem, the result will either be a single solution, infinite solutions, or no solution. We see that in this case, the two equations are equivalent to each other, which means that this system has infinite solutions (this can be visualized with a graph since both equations represent the same line).