Solve Inequality & Simul Eqns: Alg Workings Q (a,b,c)

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In summary, to solve the inequality $5(3x+1)\le 11x$, we would solve for $x$ using normal algebraic methods, keeping in mind that multiplying or dividing by a negative value changes the direction of the inequality. To solve the simultaneous equations $3x^2+y^2-7=0$ and $y-3x-5=0$, we would first substitute $y=3x+5$ into the first equation and solve for $x$, resulting in two ordered pairs that satisfy the system. Then, in
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(a) Solve the inequality 5(3x + 1) <11x, Show clear algebraic working. (2)
(b) Solve the simultaneous equations 3x 2 + y 2 – 7 = 0, y – 3x – 5 = 0 Show clear algebraic working. (4)
(c) Hence find the value of x for which 5(x + 1) < x and 3x 2 + y 2 – 7 = 0 and y – 3x – 5 = 0
 
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assuming you mean ...

(a) $5(3x+1) \le 11x$

solve for $x$ as you would any other equation ...
though probably not necessary to know in this case, be aware that multiplying or dividing by a negative value changes the direction of the inequality

(b) $3x^2 + y^2 - 7 = 0$
$y - 3x - 5 = 0 \implies y = 3x+5$

I would substitute $(3x+5)$ for $y$ in the first equation and solve the resulting quadratic for $x$ ... note you'll get two ordered pairs that satisfy the system

(c) Decide which of the two (or maybe both) values for $x$ from part (b) satisfy the given inequality
 

1. What is an inequality?

An inequality is a mathematical statement that compares two quantities using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).

2. How do you solve an inequality?

To solve an inequality, you need to isolate the variable on one side of the inequality symbol and simplify the other side. You may need to use inverse operations, such as adding, subtracting, multiplying, or dividing, to isolate the variable.

3. What is a simultaneous equation?

A simultaneous equation is a system of two or more equations with multiple variables that have the same solution. The solution to a simultaneous equation is the set of values that satisfy all of the equations in the system.

4. How do you solve simultaneous equations?

To solve simultaneous equations, you can use the substitution method, elimination method, or graphing method. In the substitution method, you solve one equation for one variable and substitute that expression into the other equation. In the elimination method, you add or subtract the equations to eliminate one of the variables. In the graphing method, you graph both equations and find the point of intersection.

5. What is the purpose of using algebraic workings?

The purpose of using algebraic workings is to show the step-by-step process of solving an inequality or simultaneous equations. This helps to ensure accuracy and allows others to follow the solution method. It also helps to identify any errors made during the solving process.

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