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What is the solution of the equation 4/3x=-6/5

What is the answer

9 answers

To solve the equation \( \frac{4}{3}x = -\frac{6}{5} \), you can follow these steps:

  1. Isolate \( x \) by multiplying both sides by the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):

    \[ x = -\frac{6}{5} \cdot \frac{3}{4} \]

  2. Multiply the fractions:

    \[ x = -\frac{6 \cdot 3}{5 \cdot 4} = -\frac{18}{20} \]

  3. Simplify the fraction:

    \[ x = -\frac{18 \div 2}{20 \div 2} = -\frac{9}{10} \]

Thus, the solution to the equation \( \frac{4}{3}x = -\frac{6}{5} \) is

\[ x = -\frac{9}{10}. \]

Ms. Garcia surveyed the students in her class to find out if they own a pet. Two-thirds of the class, or 8 students, own a pet. Complete the equation that models the total number of students,t, in Ms. Garcia’s class.

We know from the problem that two-thirds of the class owns a pet, and this amount equals 8 students.

Let's denote the total number of students in Ms. Garcia's class as \( t \). The relationship can be modeled with the equation:

\[ \frac{2}{3}t = 8 \]

This equation states that two-thirds of the total number of students equals 8.

To find the total number of students, you can solve for \( t \):

  1. Multiply both sides by \( \frac{3}{2} \) to isolate \( t \):

\[ t = 8 \times \frac{3}{2} \]

  1. Calculate the right side:

\[ t = 8 \times \frac{3}{2} = 8 \times 1.5 = 12 \]

So, the total number of students in Ms. Garcia's class is \( t = 12 \).

Julio is making lemonade to be sold at a fair. He bought 5 bags of lemons for $19.75. Complete the equation that models the cost,c, of each bag of lemons.

To find the cost \( c \) of each bag of lemons that Julio bought, we can set up the following equation based on the information provided.

Julio bought 5 bags of lemons for a total of $19.75. Thus, the relationship can be modeled with the equation:

\[ 5c = 19.75 \]

Where:

  • \( c \) is the cost of each bag of lemons,
  • \( 5c \) represents the total cost for 5 bags of lemons, which equals $19.75.

Now, to find the cost of each bag of lemons, you can solve for \( c \):

\[ c = \frac{19.75}{5} \]

Calculating this gives:

\[ c = 3.95 \]

So, the cost of each bag of lemons is $3.95.

In her science project, Martina is observing how fast kitchen condiments can be dissolved in water. She put 8.5 ounces of water into each of 5 containers. Complete the equation that models the total amount of water,w, Martina used

To model the total amount of water \( w \) that Martina used, you can set up the following equation:

\[ w = 8.5 \times 5 \]

Where:

  • \( w \) represents the total amount of water,
  • \( 8.5 \) is the amount of water (in ounces) in each container,
  • \( 5 \) is the number of containers.

Now, calculating the right side:

\[ w = 8.5 \times 5 = 42.5 \]

Thus, the total amount of water Martina used is \( w = 42.5 \) ounces.

w/_=_ answer

To express the total amount of water \( w \) used by Martina in a complete equation format, we use the notation you provided. The equation would be:

\[ w = 8.5 \times 5 \]

where \( w \) represents the total amount of water. Thus, completing your sentence:

\[ w/ = 8.5 \times 5 = 42.5 \]

So the final equation would read:

\[ w = 42.5 \]

indicating that the total amount of water used is 42.5 ounces.