Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-7}& = & -14 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+x } & = & -14 \color{red}{ -x }\color{blue}{+7+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &2x & = &-7\\\Leftrightarrow & \color{red}{2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-11}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-13x } & = & -10 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+3}& = & 7 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+10x } & = & 7 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &21x & = &4\\\Leftrightarrow & \color{red}{21}x & = &4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & -3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-x } & = & 7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 7 \color{blue}{-1} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-4}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-9x } & = & -14 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &-2x & = &-10\\\Leftrightarrow & \color{red}{-2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-10}{-2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+6}& = & -14 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+6x } & = & -14 \color{red}{ -6x }\color{blue}{-6+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &5x & = &-20\\\Leftrightarrow & \color{red}{5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-20}{5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x } & = & 1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-9}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+11x } & = & 6 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &15x & = &15\\\Leftrightarrow & \color{red}{15}x & = &15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{15}{15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & -9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-16x & = &4\\\Leftrightarrow & \color{red}{-16}x & = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)