Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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