Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+8}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-13x } & = & -7 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+5}& = & -12 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-8x } & = & -12 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &7x & = &-17\\\Leftrightarrow & \color{red}{7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & 1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-9}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9+2x } & = & -2 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+6}& = & -15 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6+15x } & = & -15 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &28x & = &-21\\\Leftrightarrow & \color{red}{28}x & = &-21\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-21}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-x } & = & 7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-9}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-3x } & = & 14 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-2x & = &23\\\Leftrightarrow & \color{red}{-2}x & = &23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{2} } & & \\ & V = \left\{ \frac{-23}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-5}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-8x } & = & -9 \color{red}{ +8x }\color{blue}{+5-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-23x & = &-4\\\Leftrightarrow & \color{red}{-23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-15}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+11x } & = & -12 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &25x & = &3\\\Leftrightarrow & \color{red}{25}x & = &3\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{3}{25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-6}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-2x } & = & -10 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+8}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & -11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)