Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{11})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{35}{11}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-770}{ \color{blue}{22} }x- \frac{70}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -770x \color{red}{-70} & = & \color{red}{-66x} +99 \\\Leftrightarrow & -770x \color{red}{-70} \color{blue}{+70} \color{blue}{+66x} & = & \color{red}{-66x} +99 \color{blue}{+66x} \color{blue}{+70} \\\Leftrightarrow & -770x+66x& = & 99+70 \\\Leftrightarrow & \color{red}{-704} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-704} & & \\\Leftrightarrow & x = \frac{-169}{704} & & \\ & V = \left\{ \frac{-169}{704} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{15}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-165} & = & \color{red}{539x} +35 \\\Leftrightarrow & -770x \color{red}{-165} \color{blue}{+165} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{+165} \\\Leftrightarrow & -770x-539x& = & 35+165 \\\Leftrightarrow & \color{red}{-1309} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-1309} & & \\\Leftrightarrow & x = \frac{-200}{1309} & & \\ & V = \left\{ \frac{-200}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{105x} +50 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & -450x-105x& = & 50-72 \\\Leftrightarrow & \color{red}{-555} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-555} & & \\\Leftrightarrow & x = \frac{22}{555} & & \\ & V = \left\{ \frac{22}{555} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{105x} +15 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +15 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & 280x-105x& = & 15-84 \\\Leftrightarrow & \color{red}{175} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{175} & & \\ & V = \left\{ \frac{-69}{175} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{4}{9})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -35x+\frac{28}{9}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x+ \frac{56}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{+56} & = & \color{red}{162x} +81 \\\Leftrightarrow & -630x \color{red}{+56} \color{blue}{-56} \color{blue}{-162x} & = & \color{red}{162x} +81 \color{blue}{-162x} \color{blue}{-56} \\\Leftrightarrow & -630x-162x& = & 81-56 \\\Leftrightarrow & \color{red}{-792} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-792} & & \\\Leftrightarrow & x = \frac{-25}{792} & & \\ & V = \left\{ \frac{-25}{792} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{10})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x-\frac{9}{10}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-99} & = & \color{red}{550x} +100 \\\Leftrightarrow & -1320x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +100 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & -1320x-550x& = & 100+99 \\\Leftrightarrow & \color{red}{-1870} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-1870} & & \\\Leftrightarrow & x = \frac{-199}{1870} & & \\ & V = \left\{ \frac{-199}{1870} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-20} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 140x \color{red}{-20} \color{blue}{+20} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+20} \\\Leftrightarrow & 140x+98x& = & 49+20 \\\Leftrightarrow & \color{red}{238} x& = & 69 \\\Leftrightarrow & x = \frac{69}{238} & & \\ & V = \left\{ \frac{69}{238} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{3})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -35x-\frac{35}{3}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{54x} +15 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{+70} \\\Leftrightarrow & -210x-54x& = & 15+70 \\\Leftrightarrow & \color{red}{-264} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-264} & & \\\Leftrightarrow & x = \frac{-85}{264} & & \\ & V = \left\{ \frac{-85}{264} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-54} & = & \color{red}{-441x} +56 \\\Leftrightarrow & -630x \color{red}{-54} \color{blue}{+54} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{+54} \\\Leftrightarrow & -630x+441x& = & 56+54 \\\Leftrightarrow & \color{red}{-189} x& = & 110 \\\Leftrightarrow & x = \frac{110}{-189} & & \\\Leftrightarrow & x = \frac{-110}{189} & & \\ & V = \left\{ \frac{-110}{189} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{5})& = & -4x+\frac{7}{9} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -4x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-180}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{-108} & = & \color{red}{-180x} +35 \\\Leftrightarrow & 675x \color{red}{-108} \color{blue}{+108} \color{blue}{+180x} & = & \color{red}{-180x} +35 \color{blue}{+180x} \color{blue}{+108} \\\Leftrightarrow & 675x+180x& = & 35+108 \\\Leftrightarrow & \color{red}{855} x& = & 143 \\\Leftrightarrow & x = \frac{143}{855} & & \\ & V = \left\{ \frac{143}{855} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{9})& = & 3x+\frac{2}{9} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-20} & = & \color{red}{27x} +2 \\\Leftrightarrow & -180x \color{red}{-20} \color{blue}{+20} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{+20} \\\Leftrightarrow & -180x-27x& = & 2+20 \\\Leftrightarrow & \color{red}{-207} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-207} & & \\\Leftrightarrow & x = \frac{-22}{207} & & \\ & V = \left\{ \frac{-22}{207} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & 3x+\frac{5}{9} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 3x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-90} & = & \color{red}{189x} +35 \\\Leftrightarrow & 1260x \color{red}{-90} \color{blue}{+90} \color{blue}{-189x} & = & \color{red}{189x} +35 \color{blue}{-189x} \color{blue}{+90} \\\Leftrightarrow & 1260x-189x& = & 35+90 \\\Leftrightarrow & \color{red}{1071} x& = & 125 \\\Leftrightarrow & x = \frac{125}{1071} & & \\ & V = \left\{ \frac{125}{1071} \right\} & \\\end{align}\)