Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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