Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+9}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-9x } & = & 14 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-7}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7-2x } & = & 1 \color{red}{ +2x }\color{blue}{+7-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-5}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-13x } & = & -6 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & 9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-12}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12+11x } & = & 8 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &15x & = &20\\\Leftrightarrow & \color{red}{15}x & = &20\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{20}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+10}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10-14x } & = & -7 \color{red}{ +14x }\color{blue}{-10-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -7 \color{blue}{-10} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+1}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1-8x } & = & -2 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-15}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15+12x } & = & 15 \color{red}{ -12x }\color{blue}{+15+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &17x & = &30\\\Leftrightarrow & \color{red}{17}x & = &30\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{30}{17} \\\Leftrightarrow & \color{green}{ x = \frac{30}{17} } & & \\ & V = \left\{ \frac{30}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-10}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+14x } & = & 11 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &19x & = &21\\\Leftrightarrow & \color{red}{19}x & = &21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-13}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13-11x } & = & -6 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &4x & = &7\\\Leftrightarrow & \color{red}{4}x & = &7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+14}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14+11x } & = & -6 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &23x & = &-20\\\Leftrightarrow & \color{red}{23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)