Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-13}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-9x } & = & 4 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-20x & = &17\\\Leftrightarrow & \color{red}{-20}x & = &17\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{17}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{20} } & & \\ & V = \left\{ \frac{-17}{20} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8-x } & = & -12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &-6x & = &-20\\\Leftrightarrow & \color{red}{-6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+10}& = & -7 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+14x } & = & -7 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -7 \color{blue}{-10} \\\Leftrightarrow &17x & = &-17\\\Leftrightarrow & \color{red}{17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-17}{17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-7}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-14x } & = & -5 \color{red}{ +14x }\color{blue}{+7-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-27x & = &2\\\Leftrightarrow & \color{red}{-27}x & = &2\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{2}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{27} } & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-11}& = & -2 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-12x } & = & -2 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-10}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-14x } & = & 7 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-23x & = &17\\\Leftrightarrow & \color{red}{-23}x & = &17\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{17}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{23} } & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+7}& = & -10 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+3x } & = & -10 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &7x & = &-17\\\Leftrightarrow & \color{red}{7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+7}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+13x } & = & -12 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &20x & = &-19\\\Leftrightarrow & \color{red}{20}x & = &-19\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-19}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{20} } & & \\ & V = \left\{ \frac{-19}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-15}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+7x } & = & -1 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &18x & = &14\\\Leftrightarrow & \color{red}{18}x & = &14\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{14}{18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+3}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-14x } & = & -7 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+15}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+13x } & = & -2 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &24x & = &-17\\\Leftrightarrow & \color{red}{24}x & = &-17\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-17}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{24} } & & \\ & V = \left\{ \frac{-17}{24} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-4}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4-13x } & = & 1 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-2x & = &5\\\Leftrightarrow & \color{red}{-2}x & = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)