Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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