Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{7})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 16x-\frac{16}{7}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-80} & = & \color{red}{-175x} +63 \\\Leftrightarrow & 560x \color{red}{-80} \color{blue}{+80} \color{blue}{+175x} & = & \color{red}{-175x} +63 \color{blue}{+175x} \color{blue}{+80} \\\Leftrightarrow & 560x+175x& = & 63+80 \\\Leftrightarrow & \color{red}{735} x& = & 143 \\\Leftrightarrow & x = \frac{143}{735} & & \\ & V = \left\{ \frac{143}{735} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{30}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+90} & = & \color{red}{231x} +44 \\\Leftrightarrow & 396x \color{red}{+90} \color{blue}{-90} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-90} \\\Leftrightarrow & 396x-231x& = & 44-90 \\\Leftrightarrow & \color{red}{165} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{165} & & \\ & V = \left\{ \frac{-46}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{275x} +25 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -660x-275x& = & 25+132 \\\Leftrightarrow & \color{red}{-935} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-935} & & \\\Leftrightarrow & x = \frac{-157}{935} & & \\ & V = \left\{ \frac{-157}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{8})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{-45} & = & \color{red}{168x} +32 \\\Leftrightarrow & 360x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +32 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & 360x-168x& = & 32+45 \\\Leftrightarrow & \color{red}{192} x& = & 77 \\\Leftrightarrow & x = \frac{77}{192} & & \\ & V = \left\{ \frac{77}{192} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{3})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{+98} & = & \color{red}{-42x} +27 \\\Leftrightarrow & 735x \color{red}{+98} \color{blue}{-98} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{-98} \\\Leftrightarrow & 735x+42x& = & 27-98 \\\Leftrightarrow & \color{red}{777} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{777} & & \\ & V = \left\{ \frac{-71}{777} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{12})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{25}{12}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{+25} & = & \color{red}{-36x} +40 \\\Leftrightarrow & 240x \color{red}{+25} \color{blue}{-25} \color{blue}{+36x} & = & \color{red}{-36x} +40 \color{blue}{+36x} \color{blue}{-25} \\\Leftrightarrow & 240x+36x& = & 40-25 \\\Leftrightarrow & \color{red}{276} x& = & 15 \\\Leftrightarrow & x = \frac{15}{276} & & \\\Leftrightarrow & x = \frac{5}{92} & & \\ & V = \left\{ \frac{5}{92} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -25x-\frac{20}{7}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{-60} & = & \color{red}{84x} +56 \\\Leftrightarrow & -525x \color{red}{-60} \color{blue}{+60} \color{blue}{-84x} & = & \color{red}{84x} +56 \color{blue}{-84x} \color{blue}{+60} \\\Leftrightarrow & -525x-84x& = & 56+60 \\\Leftrightarrow & \color{red}{-609} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-609} & & \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{11})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -14x+\frac{35}{11}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x+ \frac{70}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{+70} & = & \color{red}{-66x} +99 \\\Leftrightarrow & -308x \color{red}{+70} \color{blue}{-70} \color{blue}{+66x} & = & \color{red}{-66x} +99 \color{blue}{+66x} \color{blue}{-70} \\\Leftrightarrow & -308x+66x& = & 99-70 \\\Leftrightarrow & \color{red}{-242} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-242} & & \\\Leftrightarrow & x = \frac{-29}{242} & & \\ & V = \left\{ \frac{-29}{242} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{-90} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 504x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & 504x+105x& = & 14+90 \\\Leftrightarrow & \color{red}{609} x& = & 104 \\\Leftrightarrow & x = \frac{104}{609} & & \\ & V = \left\{ \frac{104}{609} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{49x} +9 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{-30} \\\Leftrightarrow & 210x-49x& = & 9-30 \\\Leftrightarrow & \color{red}{161} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{161} & & \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & -8x+\frac{6}{7} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{+98} & = & \color{red}{-168x} +18 \\\Leftrightarrow & 735x \color{red}{+98} \color{blue}{-98} \color{blue}{+168x} & = & \color{red}{-168x} +18 \color{blue}{+168x} \color{blue}{-98} \\\Leftrightarrow & 735x+168x& = & 18-98 \\\Leftrightarrow & \color{red}{903} x& = & -80 \\\Leftrightarrow & x = \frac{-80}{903} & & \\ & V = \left\{ \frac{-80}{903} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -8x-\frac{16}{11}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-112} & = & \color{red}{693x} +99 \\\Leftrightarrow & -616x \color{red}{-112} \color{blue}{+112} \color{blue}{-693x} & = & \color{red}{693x} +99 \color{blue}{-693x} \color{blue}{+112} \\\Leftrightarrow & -616x-693x& = & 99+112 \\\Leftrightarrow & \color{red}{-1309} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-1309} & & \\\Leftrightarrow & x = \frac{-211}{1309} & & \\ & V = \left\{ \frac{-211}{1309} \right\} & \\\end{align}\)