Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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