Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & 4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & 6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &-16x & = &18\\\Leftrightarrow & \color{red}{-16}x & = &18\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{18}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-8}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8+15x } & = & 15 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &23x & = &23\\\Leftrightarrow & \color{red}{23}x & = &23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{23}{23} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-x } & = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+11}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-4x } & = & -1 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-1}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+9x } & = & -2 \color{red}{ -9x }\color{blue}{+1+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+4}& = & 6 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+2x } & = & 6 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)