Solve equations with brackets, including those that first need to be formed from a word problem.

Find the value of the unknown in this equation.

Find the solution to this equation.

What is the solution to this equation?

What is the value of the unknown in this equation?

Identify the correct equation and solution for w if the perimeter of this regular octagon is 56 cm.

Solving equations with brackets

﻿Hello, my name is Miss Parnham. In this lesson, we're going to learn how to solve equations with unknown on both sides. Let's solve this equation using the balance method, which means doing the same to both sides of the equation. Because we have two terms that involve e and we only require one, we must eliminate the smaller one. So let's subtract three e from both sides of the equation. And that simplifies to five e subtract five equals 10. Now let's eliminate the subtract five. We do that by adding five. That gives us five e equals 15. To get e on its own, all we need to do now is divide by five. So e is three. We can form equations from problems. If we have a rectangle, and we know that the opposite sides on a rectangle are equal. So we can take these two expressions to form an equation. Just like before, we eliminate the smaller of the two unknowns. Let's subtract five f. So five equals five f subtract seven. Let's eliminate the subtract seven by adding seven. So 12 equals five f. Now let's divide by five. 2.4 equals f or if you prefer f equals 2.4. Here's some questions for you to try. Pause the video to complete the task and restart the video when you're finished. Here are the answers. In question two, we have a parallelogram. We just opposite equal angles. So setting the two expressions equal to one another, forms an equation which we can solve. Here's some more questions for you to try. Pause the video to complete the task and restart the video when you're finished. Here are the answers. In question four, we have an isosceles triangle as indicated by the markings, which means the sides are the same length. So three n plus four equals seven n plus six, forms the equation that we can solve. Let's solve this equation. You'll notice now we have brackets. In this instance, we really need to multiply those brackets out. So let's rewrite this as three g subtract 12 equals five g plus eight. Now we can eliminate the smallest g. Let's subtract it. Negative 12 equals two g plus eight. Let's subtract eight in order to eliminate the add eight. So negative 20 equals two g. Let's divide by two. Negative 10 equals g, or if you prefer g equals negative 10. Let's look at this problem. These rectangles have the same area. So four multiplied by two h subtract one, equals three multiplied by three h subtract three. We need to multiply these brackets out. So eight h subtract four equals nine h subtract nine. Let's eliminate the smallest unknown. Let's subtract eight h. So negative four equals h subtract nine. Let's add nine to eliminate the subtract nine. So five equals h or h equals five. Here are some questions for you to try. Pause the video to complete the task and restart the video when you're finished. Here are the answers. In question six, we have a pair of corresponding angles, which are equal. So setting the two expressions equal to one another, forms an equation that can be solved to find z. Here's another question for you to try. Pause the video to complete the task and restart the video when you're finished. Here are the answers. In this question, we have regular polygons, which means the sides on each polygon are equal. So the Pentagon has obviously got five sides, and that's why we have five outside the bracket containing five v subtract three. Hexagon has six sides, six outside the bracket containing three v plus one, and we solve to find v is three. That's all for this lesson. Thank you for watching.

Solve equations with unknown on both sides.

Solving equations with unknown on both sides

In this lesson, we will solve equations with an unknown on both sides including those that first need to be formed from a word problem.

Maths

Y10 Maths (Foundation)

Key Stage 4

Year 10

Miss

Solving equations 1 (One step, Two Step and Brackets)

Algebra (A)

THEME

UNIT

Solving one-step equations

Solving two-step equations

Identify the correct working and solution to find one side on this equilateral triangle.

Identify the correct working and solution to find the value of v.

Y11 Maths (Foundation)

Year 11

Revise - Solving Equations

Number (N)

Solve equations that first involve simplification 2 (x + 3) + 5x = 15

Solve simple algebraic fractions (equal to a number)

Solving algebraic fractions (equal to x + a)

Solving algebraic fractions (one fraction equal to another)

Y10 Maths (Core)

Collecting, Indices, Expand and Simplify, Solving Equations 1

Simplify Expressions by Collecting Like Terms

Simplify Expressions by Multiplying Terms

Expand a Term over a Single Bracket

Expand a Term over a Single Bracket including Powers

Expand 2 brackets and simplify expressions (Part 1)

Expand 2 brackets and simplify expressions (Part 2)

Expand and simplify double brackets

Expand and Simplify Double Brackets (Coefficient of x Greater than 1)

Multiplication Law for indices

Division Law for indices

Power Law for Indices

Combining Index Laws

Lesson overview:Solving equations with unknown on both sides

Core Content

Solving equations 1 (One step, Two Step and Brackets):