Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-8}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-3x } & = & 3 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &10x & = &11\\\Leftrightarrow & \color{red}{10}x & = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-11}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-13x } & = & -7 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+13}& = & 8 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+12x } & = & 8 \color{red}{ -12x }\color{blue}{-13+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &25x & = &-5\\\Leftrightarrow & \color{red}{25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-5}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+13}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-7x } & = & 11 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+8}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-3x } & = & 7 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & -2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+14}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-13x } & = & -11 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &x & = &-25\\\Leftrightarrow & \color{red}{}x & = &-25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -25 \\\Leftrightarrow & \color{green}{ x = -25 } & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-x } & = & 5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+2}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-13x } & = & -3 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+8}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-14x } & = & 3 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &-27x & = &-5\\\Leftrightarrow & \color{red}{-27}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-5}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{27} } & & \\ & V = \left\{ \frac{5}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+5}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-14x } & = & 11 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)