Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+13}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+8x } & = & -9 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &17x & = &-22\\\Leftrightarrow & \color{red}{17}x & = &-22\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-22}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+15}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+5x } & = & 8 \color{red}{ -5x }\color{blue}{-15+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-1}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1-4x } & = & 10 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-12}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-9x } & = & 13 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &2x & = &25\\\Leftrightarrow & \color{red}{2}x & = &25\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{25}{2} \\\Leftrightarrow & \color{green}{ x = \frac{25}{2} } & & \\ & V = \left\{ \frac{25}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+1}& = & 8 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1+3x } & = & 8 \color{red}{ -3x }\color{blue}{-1+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &4x & = &7\\\Leftrightarrow & \color{red}{4}x & = &7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+14}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-5x } & = & -15 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &x & = &-29\\\Leftrightarrow & \color{red}{}x & = &-29\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -29 \\\Leftrightarrow & \color{green}{ x = -29 } & & \\ & V = \left\{ -29 \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+11}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11+13x } & = & 2 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &21x & = &-9\\\Leftrightarrow & \color{red}{21}x & = &-9\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-9}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-4}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+3x } & = & -1 \color{red}{ -3x }\color{blue}{+4+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-8}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-14x } & = & -4 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-20\\\Leftrightarrow & \color{red}{-11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7-x } & = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-2}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-5x } & = & -3 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)