Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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