Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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