Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-1)& = & -5 \color{red}{+} (13+x) \\\Leftrightarrow & -18x-3& = &-5+13+x \\\Leftrightarrow & -18x \color{red}{-3} & = &8 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -18x-x& = &8+3 \\\Leftrightarrow & -19x& = &11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-2)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & 18x-6& = &9+6+x \\\Leftrightarrow & 18x \color{red}{-6} & = &15 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &15+6 \\\Leftrightarrow & 17x& = &21 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{21}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{21}{17} & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x+5)& = & -7 \color{red}{+} (15+x) \\\Leftrightarrow & -12x+15& = &-7+15+x \\\Leftrightarrow & -12x \color{red}{+15} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -12x-x& = &8-15 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x-7)& = & 6 \color{red}{-} (-15+x) \\\Leftrightarrow & -18x-42& = &6+15-x \\\Leftrightarrow & -18x \color{red}{-42} & = &21 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -18x+x& = &21+42 \\\Leftrightarrow & -17x& = &63 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{63}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-63}{17} & & \\ & V = \left\{ \frac{-63}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+4)& = & 13 \color{red}{+} (11+x) \\\Leftrightarrow & 6x+24& = &13+11+x \\\Leftrightarrow & 6x \color{red}{+24} & = &24 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 6x-x& = &24-24 \\\Leftrightarrow & 5x& = &0 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{0}{ \color{red}{5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-3)& = & 10 \color{red}{-} (15+x) \\\Leftrightarrow & 10x-15& = &10-15-x \\\Leftrightarrow & 10x \color{red}{-15} & = &-5 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 10x+x& = &-5+15 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x+2)& = & 11 \color{red}{+} (13+x) \\\Leftrightarrow & 20x+10& = &11+13+x \\\Leftrightarrow & 20x \color{red}{+10} & = &24 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 20x-x& = &24-10 \\\Leftrightarrow & 19x& = &14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x+1)& = & 8 \color{red}{-} (9+3x) \\\Leftrightarrow & 10x+2& = &8-9-3x \\\Leftrightarrow & 10x \color{red}{+2} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 10x+3x& = &-1-2 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+3)& = & 9 \color{red}{-} (7-5x) \\\Leftrightarrow & 18x+18& = &9-7+5x \\\Leftrightarrow & 18x \color{red}{+18} & = &2 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 18x-5x& = &2-18 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x-6)& = & 1 \color{red}{-} (-2+x) \\\Leftrightarrow & 24x-36& = &1+2-x \\\Leftrightarrow & 24x \color{red}{-36} & = &3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &3+36 \\\Leftrightarrow & 25x& = &39 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{39}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{39}{25} & & \\ & V = \left\{ \frac{39}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x-5)& = & -4 \color{red}{+} (1+x) \\\Leftrightarrow & -12x-15& = &-4+1+x \\\Leftrightarrow & -12x \color{red}{-15} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -12x-x& = &-3+15 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x-5)& = & 12 \color{red}{+} (-7+x) \\\Leftrightarrow & 8x-10& = &12-7+x \\\Leftrightarrow & 8x \color{red}{-10} & = &5 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 8x-x& = &5+10 \\\Leftrightarrow & 7x& = &15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)