Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+2)& = & -7 \color{red}{-} (-11-5x) \\\Leftrightarrow & 6x+12& = &-7+11+5x \\\Leftrightarrow & 6x \color{red}{+12} & = &4 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 6x-5x& = &4-12 \\\Leftrightarrow & x& = &-8 \\ & V = \left\{ -8 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x+2)& = & -2 \color{red}{-} (-2+4x) \\\Leftrightarrow & 3x+6& = &-2+2-4x \\\Leftrightarrow & 3x \color{red}{+6} & = &0 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & 3x+4x& = &0-6 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x+4)& = & 14 \color{red}{-} (-8+4x) \\\Leftrightarrow & -3x+12& = &14+8-4x \\\Leftrightarrow & -3x \color{red}{+12} & = &22 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & -3x+4x& = &22-12 \\\Leftrightarrow & x& = &10 \\ & V = \left\{ 10 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x+5)& = & 11 \color{red}{+} (5+x) \\\Leftrightarrow & -6x+30& = &11+5+x \\\Leftrightarrow & -6x \color{red}{+30} & = &16 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -6x-x& = &16-30 \\\Leftrightarrow & -7x& = &-14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-14}{ \color{red}{-7} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x-3)& = & -9 \color{red}{+} (-4+x) \\\Leftrightarrow & -6x-6& = &-9-4+x \\\Leftrightarrow & -6x \color{red}{-6} & = &-13 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &-13+6 \\\Leftrightarrow & -7x& = &-7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-7}{ \color{red}{-7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x+7)& = & 2 \color{red}{+} (7+x) \\\Leftrightarrow & -2x+14& = &2+7+x \\\Leftrightarrow & -2x \color{red}{+14} & = &9 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -2x-x& = &9-14 \\\Leftrightarrow & -3x& = &-5 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-5}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-6)& = & -2 \color{red}{-} (9+x) \\\Leftrightarrow & 24x-24& = &-2-9-x \\\Leftrightarrow & 24x \color{red}{-24} & = &-11 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &-11+24 \\\Leftrightarrow & 25x& = &13 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{13}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{13}{25} & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x+2)& = & 12 \color{red}{+} (2+x) \\\Leftrightarrow & 25x+10& = &12+2+x \\\Leftrightarrow & 25x \color{red}{+10} & = &14 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 25x-x& = &14-10 \\\Leftrightarrow & 24x& = &4 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{4}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{1}{6} & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+5)& = & -13 \color{red}{+} (-9-5x) \\\Leftrightarrow & 18x+30& = &-13-9-5x \\\Leftrightarrow & 18x \color{red}{+30} & = &-22 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 18x+5x& = &-22-30 \\\Leftrightarrow & 23x& = &-52 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-52}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-52}{23} & & \\ & V = \left\{ \frac{-52}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x+4)& = & 8 \color{red}{+} (2+x) \\\Leftrightarrow & -24x+24& = &8+2+x \\\Leftrightarrow & -24x \color{red}{+24} & = &10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &10-24 \\\Leftrightarrow & -25x& = &-14 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-14}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-5)& = & -6 \color{red}{+} (8+x) \\\Leftrightarrow & 6x-10& = &-6+8+x \\\Leftrightarrow & 6x \color{red}{-10} & = &2 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 6x-x& = &2+10 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+3)& = & -8 \color{red}{+} (5-3x) \\\Leftrightarrow & -10x+15& = &-8+5-3x \\\Leftrightarrow & -10x \color{red}{+15} & = &-3 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+15} \color{blue}{-15} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-15} \\\Leftrightarrow & -10x+3x& = &-3-15 \\\Leftrightarrow & -7x& = &-18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)