Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-15}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15+11x } & = & 4 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &17x & = &19\\\Leftrightarrow & \color{red}{17}x & = &19\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{19}{17} \\\Leftrightarrow & \color{green}{ x = \frac{19}{17} } & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-x } & = & -15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-11}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-13x } & = & 3 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-13x } & = & 14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-6x & = &-15\\\Leftrightarrow & \color{red}{-6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-7}& = & 14 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-10x } & = & 14 \color{red}{ +10x }\color{blue}{+7-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &3x & = &21\\\Leftrightarrow & \color{red}{3}x & = &21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{21}{3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+15}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15-5x } & = & 4 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &2x & = &-11\\\Leftrightarrow & \color{red}{2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-2}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-3x } & = & 10 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)