Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-10}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-13x } & = & -7 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-7}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+13x } & = & -2 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &12x & = &5\\\Leftrightarrow & \color{red}{12}x & = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+9}& = & -9 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+15x } & = & -9 \color{red}{ -15x }\color{blue}{-9+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &19x & = &-18\\\Leftrightarrow & \color{red}{19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+8}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-11x } & = & 1 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-10}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10+11x } & = & -13 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &20x & = &-3\\\Leftrightarrow & \color{red}{20}x & = &-3\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-3}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{20} } & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & -6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-x } & = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-1}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-11x } & = & 2 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)