Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x } & = & -2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-4x & = &22\\\Leftrightarrow & \color{red}{-4}x & = &22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-x } & = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & 5 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+14}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-10x } & = & 3 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-4}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-7x } & = & 8 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &4x & = &9\\\Leftrightarrow & \color{red}{4}x & = &9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+9}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x } & = & -14 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &23x & = &-23\\\Leftrightarrow & \color{red}{23}x & = &-23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-23}{23} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-5}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & -8 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-10x & = &-10\\\Leftrightarrow & \color{red}{-10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-10}{-10} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+7}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-5x } & = & -14 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-21\\\Leftrightarrow & \color{red}{-6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)