Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+5}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-4x } & = & 14 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & 8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+10}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-12x } & = & 3 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-23x & = &-7\\\Leftrightarrow & \color{red}{-23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+6}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-4x } & = & 8 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-16x & = &23\\\Leftrightarrow & \color{red}{-16}x & = &23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{16} } & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+9}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-14x } & = & -2 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-27x & = &-11\\\Leftrightarrow & \color{red}{-27}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-11}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{11}{27} } & & \\ & V = \left\{ \frac{11}{27} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+4}& = & -15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+6x } & = & -15 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &19x & = &-19\\\Leftrightarrow & \color{red}{19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+2}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+13x } & = & 11 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &22x & = &9\\\Leftrightarrow & \color{red}{22}x & = &9\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{9}{22} \\\Leftrightarrow & \color{green}{ x = \frac{9}{22} } & & \\ & V = \left\{ \frac{9}{22} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-x } & = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)