Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x-4)& = & -10 \color{red}{-} (9+x) \\\Leftrightarrow & -12x-12& = &-10-9-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-19+12 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x-6)& = & 13 \color{red}{-} (5+x) \\\Leftrightarrow & 24x-24& = &13-5-x \\\Leftrightarrow & 24x \color{red}{-24} & = &8 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &8+24 \\\Leftrightarrow & 25x& = &32 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{32}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{32}{25} & & \\ & V = \left\{ \frac{32}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-6)& = & -15 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x-30& = &-15-15+x \\\Leftrightarrow & 30x \color{red}{-30} & = &-30 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-30 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &-30+30 \\\Leftrightarrow & 29x& = &0 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{0}{ \color{red}{29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-2)& = & 5 \color{red}{+} (8+x) \\\Leftrightarrow & 20x-10& = &5+8+x \\\Leftrightarrow & 20x \color{red}{-10} & = &13 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &13+10 \\\Leftrightarrow & 19x& = &23 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{23}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{23}{19} & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x+1)& = & 9 \color{red}{-} (-9-5x) \\\Leftrightarrow & -6x+2& = &9+9+5x \\\Leftrightarrow & -6x \color{red}{+2} & = &18 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & -6x-5x& = &18-2 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x-6)& = & 5 \color{red}{-} (1+x) \\\Leftrightarrow & 8x-24& = &5-1-x \\\Leftrightarrow & 8x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 8x+x& = &4+24 \\\Leftrightarrow & 9x& = &28 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{28}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{28}{9} & & \\ & V = \left\{ \frac{28}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x+7)& = & -4 \color{red}{-} (-10+x) \\\Leftrightarrow & 2x+14& = &-4+10-x \\\Leftrightarrow & 2x \color{red}{+14} & = &6 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 2x+x& = &6-14 \\\Leftrightarrow & 3x& = &-8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-2)& = & -15 \color{red}{+} (-12+x) \\\Leftrightarrow & 2x-4& = &-15-12+x \\\Leftrightarrow & 2x \color{red}{-4} & = &-27 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 2x-x& = &-27+4 \\\Leftrightarrow & x& = &-23 \\ & V = \left\{ -23 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x+7)& = & -15 \color{red}{+} (-15+x) \\\Leftrightarrow & -30x+42& = &-15-15+x \\\Leftrightarrow & -30x \color{red}{+42} & = &-30 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-30 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -30x-x& = &-30-42 \\\Leftrightarrow & -31x& = &-72 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-72}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{72}{31} & & \\ & V = \left\{ \frac{72}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x-1)& = & -4 \color{red}{+} (14-5x) \\\Leftrightarrow & 6x-6& = &-4+14-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &10 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &10+6 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x+3)& = & 2 \color{red}{-} (-15+3x) \\\Leftrightarrow & 2x+6& = &2+15-3x \\\Leftrightarrow & 2x \color{red}{+6} & = &17 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 2x+3x& = &17-6 \\\Leftrightarrow & 5x& = &11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x-2)& = & 15 \color{red}{-} (15+x) \\\Leftrightarrow & -20x-8& = &15-15-x \\\Leftrightarrow & -20x \color{red}{-8} & = &0 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -20x+x& = &0+8 \\\Leftrightarrow & -19x& = &8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)