Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &6x & = &-9\\\Leftrightarrow & \color{red}{6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+2}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2+7x } & = & -4 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &19x & = &-6\\\Leftrightarrow & \color{red}{19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-10}& = & -7 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10+4x } & = & -7 \color{red}{ -4x }\color{blue}{+10+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+14}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-7x } & = & -12 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &8x & = &-26\\\Leftrightarrow & \color{red}{8}x & = &-26\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-26}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-4}& = & 13 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-2x } & = & 13 \color{red}{ +2x }\color{blue}{+4-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-9}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-10x } & = & -12 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-x } & = & 14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &-11x & = &22\\\Leftrightarrow & \color{red}{-11}x & = &22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{22}{-11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-13}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13-14x } & = & 15 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-15x & = &28\\\Leftrightarrow & \color{red}{-15}x & = &28\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{28}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{15} } & & \\ & V = \left\{ \frac{-28}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+11}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-8x } & = & -4 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &x & = &-15\\\Leftrightarrow & \color{red}{}x & = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & 15 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)