Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-6}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+6x } & = & 12 \color{red}{ -6x }\color{blue}{+6+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+9}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+7x } & = & -4 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &22x & = &-13\\\Leftrightarrow & \color{red}{22}x & = &-13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{22} } & & \\ & V = \left\{ \frac{-13}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+13}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+5x } & = & -9 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &11x & = &-22\\\Leftrightarrow & \color{red}{11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-22}{11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-7}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-7x } & = & 13 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+10}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-13x } & = & 1 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-6}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-13x } & = & -1 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-28x & = &5\\\Leftrightarrow & \color{red}{-28}x & = &5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{28} } & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-x } & = & 10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+3}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+7x } & = & 6 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &18x & = &3\\\Leftrightarrow & \color{red}{18}x & = &3\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{3}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-11x & = &25\\\Leftrightarrow & \color{red}{-11}x & = &25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{11} } & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)