Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+8}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+15x } & = & 10 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &23x & = &2\\\Leftrightarrow & \color{red}{23}x & = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-16x & = &30\\\Leftrightarrow & \color{red}{-16}x & = &30\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{30}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-25\\\Leftrightarrow & \color{red}{-6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+9}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9+7x } & = & 10 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-13}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-7x } & = & 8 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &-17x & = &21\\\Leftrightarrow & \color{red}{-17}x & = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & 5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+1}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-5x } & = & -14 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+14}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-13x } & = & 3 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+4}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4-11x } & = & 5 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+5}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5+14x } & = & -3 \color{red}{ -14x }\color{blue}{-5+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &29x & = &-8\\\Leftrightarrow & \color{red}{29}x & = &-8\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-8}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{29} } & & \\ & V = \left\{ \frac{-8}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+8}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-3x } & = & -5 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)