Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & -8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-1}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1+13x } & = & 12 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+7}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+7x } & = & -7 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &22x & = &-14\\\Leftrightarrow & \color{red}{22}x & = &-14\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-14}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+8}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+5x } & = & 12 \color{red}{ -5x }\color{blue}{-8+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-4}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+4x } & = & 4 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+12}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+2x } & = & -2 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-12}& = & 1 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+4x } & = & 1 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-3}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & -1 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+6}& = & 3 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+8x } & = & 3 \color{red}{ -8x }\color{blue}{-6+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-24\\\Leftrightarrow & \color{red}{-5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)