Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-10}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10-14x } & = & -10 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-5}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5-7x } & = & 9 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &4x & = &14\\\Leftrightarrow & \color{red}{4}x & = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-9}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-9x } & = & 6 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+9}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-5x } & = & -1 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-4}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+11x } & = & -14 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &26x & = &-10\\\Leftrightarrow & \color{red}{26}x & = &-10\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-10}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-14}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & 11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &-13x & = &25\\\Leftrightarrow & \color{red}{-13}x & = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+7}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-13x } & = & -13 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-20\\\Leftrightarrow & \color{red}{-11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-3}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-4x } & = & 7 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-6}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+5x } & = & 8 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &16x & = &14\\\Leftrightarrow & \color{red}{16}x & = &14\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{14}{16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+2}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2-3x } & = & 1 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)