Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+14}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x } & = & 11 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-3\\\Leftrightarrow & \color{red}{-25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+7}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-5x } & = & 1 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+12}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12-14x } & = & -6 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-12}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-7x } & = & -2 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-20x & = &10\\\Leftrightarrow & \color{red}{-20}x & = &10\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{10}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+10}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-5x } & = & 11 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+8}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8-4x } & = & -8 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+2}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-3x } & = & 12 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+2}& = & 3 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+6x } & = & 3 \color{red}{ -6x }\color{blue}{-2+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & 8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+12}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+7x } & = & -14 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &15x & = &-26\\\Leftrightarrow & \color{red}{15}x & = &-26\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-26}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{15} } & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+11}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11+3x } & = & 9 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)