Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+12}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12-7x } & = & -15 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &8x & = &-27\\\Leftrightarrow & \color{red}{8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-27}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{8} } & & \\ & V = \left\{ \frac{-27}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & 1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+10}& = & 9 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+14x } & = & 9 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-13}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13-14x } & = & -9 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-9}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+15x } & = & 15 \color{red}{ -15x }\color{blue}{+9+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &19x & = &24\\\Leftrightarrow & \color{red}{19}x & = &24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{24}{19} } & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+6}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-9x } & = & 14 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+14}& = & 6 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-8x } & = & 6 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+15}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-9x } & = & 14 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+10}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-7x } & = & -13 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &3x & = &-23\\\Leftrightarrow & \color{red}{3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & -4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & -15 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-29\\\Leftrightarrow & \color{red}{-6}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-29}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{29}{6} } & & \\ & V = \left\{ \frac{29}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+9}& = & 5 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9+10x } & = & 5 \color{red}{ -10x }\color{blue}{-9+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)