Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+3}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3-7x } & = & 13 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-x } & = & -12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &5x & = &-24\\\Leftrightarrow & \color{red}{5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+5}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-3x } & = & 1 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+1}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-7x } & = & 13 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+6}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x } & = & -10 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+12}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-13x } & = & 12 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-28x & = &0\\\Leftrightarrow & \color{red}{-28}x & = &0\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{0}{-28} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-8}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+8x } & = & -9 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-9}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-3x } & = & -10 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-1}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & -14 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &-25x & = &-13\\\Leftrightarrow & \color{red}{-25}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{13}{25} } & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+14}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-5x } & = & 6 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &5x & = &-29\\\Leftrightarrow & \color{red}{5}x & = &-29\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-29}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{5} } & & \\ & V = \left\{ \frac{-29}{5} \right\} & \\\end{align}\)