Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-x } & = & 11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-12}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12+11x } & = & 5 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &23x & = &17\\\Leftrightarrow & \color{red}{23}x & = &17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{17}{23} } & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+12}& = & -5 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+9x } & = & -5 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-9}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-11x } & = & -3 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & 6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & 5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+12}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12-5x } & = & 3 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &-2x & = &-9\\\Leftrightarrow & \color{red}{-2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)