Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+14}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x } & = & -3 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-17\\\Leftrightarrow & \color{red}{-20}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-17}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-9}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+11x } & = & -14 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &26x & = &-5\\\Leftrightarrow & \color{red}{26}x & = &-5\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-5}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{26} } & & \\ & V = \left\{ \frac{-5}{26} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+6}& = & -8 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+10x } & = & -8 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &9x & = &-14\\\Leftrightarrow & \color{red}{9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+3}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-7x } & = & -4 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-17x & = &-7\\\Leftrightarrow & \color{red}{-17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-2}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+9x } & = & -13 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & 12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-15}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-3x } & = & -9 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-9}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-7x } & = & 3 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-25\\\Leftrightarrow & \color{red}{-8}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-25}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{25}{8} } & & \\ & V = \left\{ \frac{25}{8} \right\} & \\\end{align}\)