Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-4x-1=11+13x\)
2. \(-7x-2=-14+x\)
3. \(-9x-11=9+5x\)
4. \(-13x+10=-14+x\)
5. \(2x+12=10+x\)
6. \(11x-11=11+14x\)
7. \(14x-10=-15-13x\)
8. \(-14x-10=9+x\)
9. \(-13x+11=14+7x\)
10. \(-3x+14=13+x\)
11. \(-15x-10=-13+8x\)
12. \(15x+1=-12-11x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-1}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-13x } & = & 11 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-17x & = &12\\\Leftrightarrow & \color{red}{-17}x & = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-11}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-5x } & = & 9 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-14x & = &20\\\Leftrightarrow & \color{red}{-14}x & = &20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & -14 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-24\\\Leftrightarrow & \color{red}{-14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-11}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-14x } & = & 11 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &-3x & = &22\\\Leftrightarrow & \color{red}{-3}x & = &22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{3} } & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-10}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10+13x } & = & -15 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &27x & = &-5\\\Leftrightarrow & \color{red}{27}x & = &-5\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-5}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{27} } & & \\ & V = \left\{ \frac{-5}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+11}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-7x } & = & 14 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-20x & = &3\\\Leftrightarrow & \color{red}{-20}x & = &3\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{3}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{20} } & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & 13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-10}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-8x } & = & -13 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-23x & = &-3\\\Leftrightarrow & \color{red}{-23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+1}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+11x } & = & -12 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &26x & = &-13\\\Leftrightarrow & \color{red}{26}x & = &-13\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-13}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)