Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+12}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-8x } & = & -15 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-23x & = &-27\\\Leftrightarrow & \color{red}{-23}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-27}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{27}{23} } & & \\ & V = \left\{ \frac{27}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-13}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+13x } & = & 2 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &12x & = &15\\\Leftrightarrow & \color{red}{12}x & = &15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-9}& = & -6 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9+9x } & = & -6 \color{red}{ -9x }\color{blue}{+9+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & 2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+9}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-14x } & = & -3 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-23x & = &-12\\\Leftrightarrow & \color{red}{-23}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-12}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{12}{23} } & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-15}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15+7x } & = & 4 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &15x & = &19\\\Leftrightarrow & \color{red}{15}x & = &19\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{19}{15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-11}& = & -7 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+15x } & = & -7 \color{red}{ -15x }\color{blue}{+11+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-6}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-13x } & = & 9 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &-18x & = &15\\\Leftrightarrow & \color{red}{-18}x & = &15\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{15}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+9}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9+7x } & = & 2 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)