Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-8}& = & 7 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-10x } & = & 7 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-23x & = &15\\\Leftrightarrow & \color{red}{-23}x & = &15\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{15}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-6x & = &-18\\\Leftrightarrow & \color{red}{-6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-18}{-6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-1}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1+5x } & = & -13 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &16x & = &-12\\\Leftrightarrow & \color{red}{16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-12}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+6}& = & 8 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+9x } & = & 8 \color{red}{ -9x }\color{blue}{-6+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &16x & = &2\\\Leftrightarrow & \color{red}{16}x & = &2\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{2}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-14}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-14x } & = & 12 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-23x & = &26\\\Leftrightarrow & \color{red}{-23}x & = &26\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{26}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{23} } & & \\ & V = \left\{ \frac{-26}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+6}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-14x } & = & -4 \color{red}{ +14x }\color{blue}{-6-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & 6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+2}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-14x } & = & 12 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & 6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)