Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+13}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+13x } & = & 2 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &24x & = &-11\\\Leftrightarrow & \color{red}{24}x & = &-11\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-11}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{24} } & & \\ & V = \left\{ \frac{-11}{24} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+2}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2-11x } & = & 4 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &12x & = &-2\\\Leftrightarrow & \color{red}{12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-2}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & -2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-13\\\Leftrightarrow & \color{red}{-8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-4}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-6x } & = & 3 \color{red}{ +6x }\color{blue}{+4-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+1}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-2x } & = & -10 \color{red}{ +2x }\color{blue}{-1-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & -13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-27\\\Leftrightarrow & \color{red}{-4}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-27}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-7}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-4x } & = & -15 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-7}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+11x } & = & -13 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+3}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3+13x } & = & 12 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &27x & = &9\\\Leftrightarrow & \color{red}{27}x & = &9\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{9}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+10}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-5x } & = & -13 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-23\\\Leftrightarrow & \color{red}{-12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)