Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+15}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-13x } & = & -15 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-30\\\Leftrightarrow & \color{red}{-5}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-30}{-5} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+8}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-6x } & = & 5 \color{red}{ +6x }\color{blue}{-8-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+12}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-13x } & = & -9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-9}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-9x } & = & 7 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-6}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-9x } & = & 5 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+11}& = & -12 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11+4x } & = & -12 \color{red}{ -4x }\color{blue}{-11+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &13x & = &-23\\\Leftrightarrow & \color{red}{13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+11}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-7x } & = & -12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &3x & = &-23\\\Leftrightarrow & \color{red}{3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x } & = & 10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-3}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+7x } & = & 2 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &22x & = &5\\\Leftrightarrow & \color{red}{22}x & = &5\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{5}{22} \\\Leftrightarrow & \color{green}{ x = \frac{5}{22} } & & \\ & V = \left\{ \frac{5}{22} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-15}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15+11x } & = & -2 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &17x & = &13\\\Leftrightarrow & \color{red}{17}x & = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)