Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &7x & = &-11\\\Leftrightarrow & \color{red}{7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+14}& = & 13 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+14x } & = & 13 \color{red}{ -14x }\color{blue}{-14+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-7}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-5x } & = & -11 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & 12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &2x & = &-1\\\Leftrightarrow & \color{red}{2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-15}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-13x } & = & 5 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &-28x & = &20\\\Leftrightarrow & \color{red}{-28}x & = &20\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{20}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+11}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-7x } & = & -6 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-20x & = &-17\\\Leftrightarrow & \color{red}{-20}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-17}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+14}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+13x } & = & -12 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &23x & = &-26\\\Leftrightarrow & \color{red}{23}x & = &-26\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-26}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{23} } & & \\ & V = \left\{ \frac{-26}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & -7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-11}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+14x } & = & 12 \color{red}{ -14x }\color{blue}{+11+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &29x & = &23\\\Leftrightarrow & \color{red}{29}x & = &23\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{23}{29} \\\Leftrightarrow & \color{green}{ x = \frac{23}{29} } & & \\ & V = \left\{ \frac{23}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+3}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-14x } & = & -6 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-27x & = &-9\\\Leftrightarrow & \color{red}{-27}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-9}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)