Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Exercises in solving simultaneous equations with 2 variables.

Semi-worked example of solving simultaneous equations using matrices. Equation values are randomly generated. The student is walked through the steps needed to solve the equations.

Practise solving simultaneous linear equations graphically and algebraically.

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Solve unknown on one side

Solve $\displaystyle ay + b = cy + d$ for $y$.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve $\displaystyle ax + b = cx + d$ for $x$.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve $\displaystyle ax + b =\frac{f}{g}( cx + d)$ for $x$.

A video is included in Show steps which goes through a similar example.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Contains a video solving a similar quotient rule example. Although does not explicitly find $g(x)$ as asked in the question, but this is obvious.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $\log(ax+b)-\log(cx+d)=s$

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$.

Contains a video solving a similar example.

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For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

Taken from question 37 of the book Problem Solving in GCSE Mathematics by Daniel Griller.

Given bearings and lengths of two straight lines, work out the bearing and distance back to the starting point.

A Eukleides diagram shows the setup visually.

$f(x)= ae^{-bt}+c$ is given and plotted. A few points are plotted on the curve. $x$-coordinates are provided for two of them and $y$-coordinate provided for third. Student is required to determine other coordinates.

Some quadratics are to be solved by factorising

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.