Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{20}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-160} & = & \color{red}{-280x} +49 \\\Leftrightarrow & -672x \color{red}{-160} \color{blue}{+160} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{+160} \\\Leftrightarrow & -672x+280x& = & 49+160 \\\Leftrightarrow & \color{red}{-392} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-392} & & \\\Leftrightarrow & x = \frac{-209}{392} & & \\ & V = \left\{ \frac{-209}{392} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{7})& = & 4x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{25}{7}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{75}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-75} & = & \color{red}{84x} +14 \\\Leftrightarrow & -315x \color{red}{-75} \color{blue}{+75} \color{blue}{-84x} & = & \color{red}{84x} +14 \color{blue}{-84x} \color{blue}{+75} \\\Leftrightarrow & -315x-84x& = & 14+75 \\\Leftrightarrow & \color{red}{-399} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-399} & & \\\Leftrightarrow & x = \frac{-89}{399} & & \\ & V = \left\{ \frac{-89}{399} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+54} & = & \color{red}{-165x} +110 \\\Leftrightarrow & -792x \color{red}{+54} \color{blue}{-54} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{-54} \\\Leftrightarrow & -792x+165x& = & 110-54 \\\Leftrightarrow & \color{red}{-627} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-627} & & \\\Leftrightarrow & x = \frac{-56}{627} & & \\ & V = \left\{ \frac{-56}{627} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-30} \\\Leftrightarrow & -330x+231x& = & 44-30 \\\Leftrightarrow & \color{red}{-99} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-99} & & \\\Leftrightarrow & x = \frac{-14}{99} & & \\ & V = \left\{ \frac{-14}{99} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 12x-\frac{20}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-20} & = & \color{red}{49x} +2 \\\Leftrightarrow & 84x \color{red}{-20} \color{blue}{+20} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+20} \\\Leftrightarrow & 84x-49x& = & 2+20 \\\Leftrightarrow & \color{red}{35} x& = & 22 \\\Leftrightarrow & x = \frac{22}{35} & & \\ & V = \left\{ \frac{22}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{8}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+8} & = & \color{red}{77x} +6 \\\Leftrightarrow & 88x \color{red}{+8} \color{blue}{-8} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-8} \\\Leftrightarrow & 88x-77x& = & 6-8 \\\Leftrightarrow & \color{red}{11} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-36} & = & \color{red}{-154x} +99 \\\Leftrightarrow & 660x \color{red}{-36} \color{blue}{+36} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{+36} \\\Leftrightarrow & 660x+154x& = & 99+36 \\\Leftrightarrow & \color{red}{814} x& = & 135 \\\Leftrightarrow & x = \frac{135}{814} & & \\ & V = \left\{ \frac{135}{814} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{+84} & = & \color{red}{-315x} +50 \\\Leftrightarrow & 560x \color{red}{+84} \color{blue}{-84} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-84} \\\Leftrightarrow & 560x+315x& = & 50-84 \\\Leftrightarrow & \color{red}{875} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{875} & & \\ & V = \left\{ \frac{-34}{875} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{8})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 15x-\frac{15}{8}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-15} & = & \color{red}{-56x} +18 \\\Leftrightarrow & 120x \color{red}{-15} \color{blue}{+15} \color{blue}{+56x} & = & \color{red}{-56x} +18 \color{blue}{+56x} \color{blue}{+15} \\\Leftrightarrow & 120x+56x& = & 18+15 \\\Leftrightarrow & \color{red}{176} x& = & 33 \\\Leftrightarrow & x = \frac{33}{176} & & \\\Leftrightarrow & x = \frac{3}{16} & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+110} & = & \color{red}{539x} +42 \\\Leftrightarrow & -770x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -770x-539x& = & 42-110 \\\Leftrightarrow & \color{red}{-1309} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1309} & & \\\Leftrightarrow & x = \frac{4}{77} & & \\ & V = \left\{ \frac{4}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{7})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-90} & = & \color{red}{-441x} +49 \\\Leftrightarrow & -378x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +49 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & -378x+441x& = & 49+90 \\\Leftrightarrow & \color{red}{63} x& = & 139 \\\Leftrightarrow & x = \frac{139}{63} & & \\ & V = \left\{ \frac{139}{63} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{9})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{4}{9}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-28} & = & \color{red}{-189x} +36 \\\Leftrightarrow & -504x \color{red}{-28} \color{blue}{+28} \color{blue}{+189x} & = & \color{red}{-189x} +36 \color{blue}{+189x} \color{blue}{+28} \\\Leftrightarrow & -504x+189x& = & 36+28 \\\Leftrightarrow & \color{red}{-315} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-315} & & \\\Leftrightarrow & x = \frac{-64}{315} & & \\ & V = \left\{ \frac{-64}{315} \right\} & \\\end{align}\)