/* Base Styles (Mobile First) */
.r-container {
font-family: ‘Inter’, Arial, sans-serif;
color: #515151;
max-width: 1300px;
margin: 0 auto;
}
.r-section {
padding: 40px 20px;
}
.r-section-title {
font-size: 2.2em;
color: #00463a;
margin-top: 0;
margin-bottom: 30px;
font-weight: 700;
line-height: 1.2;
text-align: center;
}
.r-section-subtitle {
font-size: 1.2em;
max-width: 800px;
margin: 0 auto 30px auto;
line-height: 1.7;
text-align: center;
}
.r-faq-grid {
max-width: 800px;
margin: 0 auto;
display: grid;
gap: 20px;
}
.r-faq-item {
background-color: #f7f6f5;
border-left: 6px solid #92d0ff;
padding: 20px 25px;
border-radius: 16px;
}
.r-faq-question {
font-size: 1.15em;
margin-top: 0;
font-weight: 600;
color: #00463a;
}
.r-faq-answer {
line-height: 1.7;
font-size: 1.1em;
margin-bottom: 0;
}
.r-grid {
display: grid;
grid-template-columns: 1fr;
gap: 30px;
max-width: 1100px;
margin: 0 auto;
}
.r-card {
background-color: #ffffff;
padding: 25px;
border-radius: 16px;
}
.r-card h3 {
font-size: 1.5em;
color: #00463a;
margin-top: 0;
}
.r-card p, .r-card li {
line-height: 1.6;
font-size: 1.1em;
}
.r-card ol { padding-left: 20px; }
.r-details {
background-color: #f7f6f5;
border-radius: 16px;
margin-top: 30px;
}
.r-details summary {
font-weight: 700;
font-size: 1.2em;
color: #00463a;
padding: 20px;
cursor: pointer;
}
.r-details-content {
padding: 0 20px 20px 20px;
border-top: 1px solid #d1d1d1;
}
.r-rule-box {
background-color: #defcd1;
padding: 15px;
border-radius: 8px;
font-size: 1.2em;
font-weight: 600;
text-align: center;
color: #00463a;
margin: 15px 0;
}
/* Desktop Styles */
@media (min-width: 768px) {
.r-section {
padding: 60px 40px;
}
.r-section-title {
font-size: 2.5em;
}
.r-section-subtitle {
font-size: 1.3em;
}
.r-grid.two-col {
grid-template-columns: repeat(2, 1fr);
}
}
Solving Linear Equations
How do apps work out taxi fares or how do shops calculate discounts? These everyday problems are often solved using linear equations. Think of it like being a detective trying to find a hidden value. This guide will help you crack the code!
What’s a Linear Equation?
An equation is a statement that two things are equal, like a perfectly balanced set of scales. A linear equation is one where the highest power of the unknown variable (like $x$) is 1. The goal is to find the value of the unknown that makes the equation true.
How to Solve Linear Equations
The golden rule is: whatever you do to one side, you must do to the other. We use inverse operations (like addition and subtraction) to “undo” the equation and find the unknown.
Type 1: Simple Equations
To solve $x + 5 = 12$, we want to get $x$ by itself. The inverse of adding 5 is subtracting 5.
$x + 5 – 5 = 12 – 5$
$x = 7$
To solve $3x = 15$, we want to undo multiplying by 3. The inverse is dividing by 3.
$\frac{3x}{3} = \frac{15}{3}$
$x = 5$
Type 2: Unknowns on Both Sides
To solve $6x – 5 = 2x + 15$, first gather the $x$ terms on one side. It’s often easiest to move the smaller one.
- Subtract $2x$ from both sides: $4x – 5 = 15$
- Add 5 to both sides: $4x = 20$
- Divide by 4: $x = 5$
Type 3: Equations with Brackets
To solve $3(x+4) = 21$, your first step is always to expand the bracket.
- Expand the bracket: $3x + 12 = 21$
- Subtract 12 from both sides: $3x = 9$
- Divide by 3: $x = 3$
Type 4: Combined Equations
To solve $2(x – 3) = 4x + 2$, you combine all the steps.
- Expand the bracket: $2x – 6 = 4x + 2$
- Subtract $2x$ from both sides: $-6 = 2x + 2$
- Subtract 2 from both sides: $-8 = 2x$
- Divide by 2: $-4 = x$
Tutor Insights
🤔 Common Misunderstandings
- Sign Errors: Forgetting to change the sign when moving a term across the equals sign (e.g., moving $+5$ across means it becomes $-5$).
- Incorrectly Expanding Brackets: Writing $2(x+3)$ as $2x+3$ instead of $2x+6$. Remember to multiply everything inside!
📝 Common Exam Mistakes
- Simple Arithmetic Errors: Even with a perfect method, a small calculation mistake can cost marks.
- Not Showing Working: You can get method marks for logical steps even if your final answer is wrong.
- Forgetting to Check: If you have time, substitute your answer back into the original equation to see if it works.
Practice Questions
- Solve: $x + 12 = 20$
- Solve: $6y = 42$
- Solve: $4a – 5 = 19$
- Solve: $2(m + 7) = 22$
- Solve: $5x – 3 = 2x + 9$
Show Answers
- Answer: $x = 8$
- Answer: $y = 7$
- Answer: $a = 6$
- Answer: $m = 4$
- Answer: $x = 4$
