Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+7}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-5x } & = & -2 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+7}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & 3 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+5}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-14x } & = & -1 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-23x & = &-6\\\Leftrightarrow & \color{red}{-23}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-6}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-x } & = & -10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-9}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-14x } & = & -9 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-2}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2-x } & = & 10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-1}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-7x } & = & 5 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+9}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-13x } & = & -3 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x } & = & 6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &11x & = &14\\\Leftrightarrow & \color{red}{11}x & = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)