Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+13}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-11x } & = & 6 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-18x & = &-7\\\Leftrightarrow & \color{red}{-18}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-7}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{18} } & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = & -2 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-2x } & = & -2 \color{red}{ +2x }\color{blue}{+2-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+13}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13-13x } & = & -10 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+15}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-11x } & = & -9 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-24\\\Leftrightarrow & \color{red}{-13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+11}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-8x } & = & 14 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-5}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+13x } & = & -13 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &20x & = &-8\\\Leftrightarrow & \color{red}{20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-8}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x } & = & 3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-9}& = & -15 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+10x } & = & -15 \color{red}{ -10x }\color{blue}{+9+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & -4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+3}& = & -4 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3+8x } & = & -4 \color{red}{ -8x }\color{blue}{-3+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & 5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)