Tutor profile: Kirsten D.
Solve for x. 3x - 4 = x - 10
In order to solve for x, we need to get x on a side by itself. Right now we have a 3x on the left side of the equation and x on the right side. In order to get all the x terms on the same side, I will subtract x from both sides canceling out the x on the right hand side of the equation. 3x - 4 - x = x - 10 - x. Let's reorder the terms putting the x terms next to each other. 3x - x - 4 = x - x -10 Combining like terms, we get 2x - 4 = -10. We still want to isolate the x (get it on a side by itself). To do that we want to get rid of the -4 on the left side of the equation. To cancel the -4, we'll add 4 to both sides. 2x - 4 + 4 = -10 + 4 which gives 2x = -6. To isolate the x, divide both sides by 2. 2x/2 = -6/2 giving x = -3. Great job!!
Subject: Basic Math
Reduce 9/15 to lowest terms.
If a fraction is in lowest terms, nothing divides evenly into both the numerator and denominator except 1. Let's check if this fraction is in lowest terms. What numbers divide evenly into 9 (called factors of 9): 1, 3, 9 What numbers divide evenly into 15 (called factors of 15): 1, 3, 5, 15 Do they have any factors in common? YES! Both numbers are divisible by 3. Dividing 9 by 3 we get 3. Dividing 15 by 3 we get 5. 9/15 = 3/5. Are we finished? Do any numbers divide evenly into both 3 and 5? No! The fraction in lowest terms is 3/5.
Find the equation of the line that passes through the points (-2 , -1) and (5 , 13). Write the equation of the line in slope-intercept form.
The question asks us to write the final answer in slope-intercept form. Recall - the equation of a line written in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept of the line. In order to answer the question, we need to find both the slope (m) and the y-intercept (b). 1. First, let's find the slope: Recall - the formula to find the slope of a line is m = (y2-y1) / (x2-x1), where (x1,y1) and (x2,y2) are points on the line. It does not matter which point we call (x1,y1) and which we call (x2,y2). Let (x1,y1) = (-2,-1) and (x2,y2) = (5,13). So, x1 = -2, y1 = -1, x2 = 5, and y2 = 13. Substituting in the slope formula, we get m = (13 - (-1)) / (5 - (-2)). Remember when subtracting a negative like [13 - (-1)] it becomes 13 + 1 and [5 - (-2)] becomes 5 + 2. m = (13 + 1)/(5 + 2) = (14)/(7) = 14/7 = 2. So, the slope is 2. Remember, m = 2. 2. Second, let's find the y - intercept: Recall - we will need to use the point-slope equation of a line. (y - y1) = m(x - x1). We want the y and the x to remain variables. We know x1 = -2, y1 = -1 and m = 2. Substituting the values in, we get: y - (-1)) = 2(x - (-2)). Remember that subtracting a negative gives y + 1 = 2(x + 2). Distributing the 2 gives y + 1 = 2x + 4. We want to get y by itself by subtracting 1 from both sides. y + 1 - 1 = 2x + 4 - 1 y = 2x + 3. Is it in the correct form? Yes! So, the final answer is y = 2x + 3. Good work!
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