Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+12}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-7x } & = & 2 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-3}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-11x } & = & -1 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+2}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2+13x } & = & -10 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &24x & = &-12\\\Leftrightarrow & \color{red}{24}x & = &-12\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-12}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-2}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+3x } & = & -11 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-1}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-13x } & = & 15 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+2}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-4x } & = & -7 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+7}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+13x } & = & 1 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &23x & = &-6\\\Leftrightarrow & \color{red}{23}x & = &-6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{23} } & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & -10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & 12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-x } & = & -9 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &13x & = &-24\\\Leftrightarrow & \color{red}{13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)